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The inverse problem associated with Diffuse optical tomography image reconstruction is known to be highly nonlinear, under-determined, and ill-posed. The Levenberg-Marquardt technique is employed in solving it and is known to produce low-resolution reconstructed images. To stabilize the inversion of the large matrix, a heuristically chosen regularization parameter is used. A novel methodology is developed using Gauss-Seidel, Modified Richardson, and Kaczmarz recursive methods to solve the inverse problem and to obtain spatially varying regularization parameters, which are optimally obtained for every node automatically, which is otherwise not possible. The proposed methods are thoroughly compared with the existing traditional methods in both 2-D and 3-D imaging domains using numerically simulated noisy data and also real-life phantom data. Of all the proposed methods, the Gauss-Seidel-based method provides a quantitatively accurate estimation of spatially varying regularization using the model-resolution-matrix-based method and hence improves the quality of the reconstructed images with better resolution characteristics. [ABSTRACT FROM AUTHOR]

This work compares three nonlinear solution methods for the performance of an induction motor's magnetic equivalent circuit model with magnetic saturation. The interrelation between magnetic flux density and permeability introduces nonlinearities in the differential system of equations. Three popular nonlinear solution methods are selected for comparison, namely (i) the Gauss–Seidel method, (ii) the Newton–Raphson method and (iii) the inverse Broyden's method. While all three methods have been applied in this context before, no comparison study has been published to the authors' best knowledge. The study finds that the inverse Broyden's method is most performant in terms of the number of required iterations, the computation time per iteration and the resulting total computation time. However, for substantial saturation levels, the authors recommend a hybrid implementation of multiple solution methods to obtain robust and reliable convergence. [ABSTRACT FROM AUTHOR]

We introduce an efficient first-order primal-dual method for the solution of nonsmooth PDE-constrained optimization problems. We achieve this efficiency through not solving the PDE or its linearisation on each iteration of the optimization method. Instead, we run the method interwoven with a simple conventional linear system solver (Jacobi, Gauss–Seidel, conjugate gradients), always taking only one step of the linear system solver for each step of the optimization method. The control parameter is updated on each iteration as determined by the optimization method. We prove linear convergence under a second-order growth condition, and numerically demonstrate the performance on a variety of PDEs related to inverse problems involving boundary measurements. [ABSTRACT FROM AUTHOR]

The GMRES algorithm of Saad and Schultz [SIAM J. Sci. Stat. Comput., 7 (1986), pp. 856-869] is an iterative method for approximately solving linear systems Ax = b, with initial guess x0 and residual r0 = b Ax0. The algorithm employs the Arnoldi process to generate the Krylov basis vectors (the columns of Vκ). It is well known that this process can be viewed as a QR factorization of the matrix Bκ = [ r0, AVκ] at each iteration. Despite an O (ε)κ (Bκ) loss of orthogonality, for unit roundoff ε and condition number κ, the modified Gram-Schmidt formulation was shown to be backward stable in the seminal paper by Paige et al. [SIAM J. Matrix Anal. Appl., 28 (2006), pp. 264-284]. We present an iterated Gauss-Seidel formulation of the GMRES algorithm (IGS-GMRES) based on the ideas of Ruhe [Linear Algebra Appl., 52 (1983), pp. 591-601] and Świrydowicz et al. [Numer. Linear Algebra Appl., 28 (2020), pp. 1-20]. IGS-GMRES maintains orthogonality to the level O (ε)κ (Bκ) or O (ε), depending on the choice of one or two iterations; for two Gauss-Seidel iterations, the computed Krylov basis vectors remain orthogonal to working accuracy and the smallest singular value of Vκ remains close to one. The resulting GMRES method is thus backward stable. We show that IGS-GMRES can be implemented with only a single synchronization point per iteration, making it relevant to large-scale parallel computing environments. We also demonstrate that, unlike MGS-GMRES, in IGS-GMRES the relative Arnoldi residual corresponding to the computed approximate solution no longer stagnates above machine precision even for highly nonnormal systems. [ABSTRACT FROM AUTHOR]

Power-Hardware-in-the-Loop (PHIL) is a kind of real-time simulation, capable of exchanging not just low-voltage, low current signals, but the power required by the power device under test (PDuT). PHIL requires a PDuT to be connected to a real-time digital power network simulator via a power interface (PI). There have been quite a few PIs proposed in the past. Among them, the ideal transformer model (ITM) is the most commonly used due to its ease of implementation. Other PIs such as partial circuit duplication and damping impedance can be considered as an extended version of the ITM. These PIs need to follow a strict impedance ratio between PDuT and the rest of the system prior to the PHIL implementation, which could be a tedious and difficult task. This paper proposed a new PI for PHIL based on multi-dimensional golden section search algorithm, which can eliminate such a constraint. The proposed method has been shown to have wider stability regions when PDuT is a passive device or active one such as an inverter based resource. Moreover, dynamic responses of the proposed method are similar to those of the ITM under stable conditions. The validity of the proposed method has been justified with offline simulation and experimental PHIL setups.

The Recursive Gauss-Seidel (RGS) algorithm is presented that is implemented in a one-step Gauss-Seidel iteration for the identification of Wiener output error systems. The RGS algorithm has lower processing intensity than the popular Recursive Least Squares (RLS) algorithm due to its implementation using one-step Gauss-Seidel iteration in a sampling interval. The noise-free output samples in the data vector used for implementation of the RGS algorithm are estimated using an auxiliary model. Also, a stochastic convergence analysis is presented, and it is shown that the presented auxiliary model-based RGS algorithm gives unbiased parameter estimates even if the measurement noise is coloured. Finally, the effectiveness of the RGS algorithm is verified and compared with the equivalent RLS algorithm by computer simulations.

Load flow is an important tool for studying, designing, and analyzing power systems. It allows power system engineers to determine whether the operation and configuration of the power system is safe under varying loading conditions. It is necessary to model and simulate such a system in order to determine the power flow and losses. This research paper focuses on using numerical methods such as Newton Raphson and Gauss Seidel power flow equations for load flow analysis to calculate bus voltage magnitudes, phase angles, real and reactive power of each bus of an IEEE 9-bus test system. Newton Raphson’s computation offers fast, accurate convergence but demands complex implementation, whereas Gauss Siedel is simpler but converges slower with lower accuracy. The analysis was carried out using a MATLAB program. By manipulating variables such as power injections, voltage magnitudes, and phase angles, it solves nonlinear equations iteratively to establish stable operating points which aids in enhancing power system analysis. The line losses for the two methods are compared and the system's total load and generation power are also displayed. The consideration of line losses and assessment of total load generation is crucial for maintaining system efficiency, reliability and preventing voltage instability and equipment damage. The results are also used to generate a directed graph which shows the interconnected nature of the power system, aiding engineers in understanding power flow paths, identifying potential issues, and making informed decisions about system operations. The Newton Raphson method yields the lowest loss, with 4.585MW and 10.789Mvar. In comparison, the Gauss Seidel method achieved 4.809MW and 10.798Mvar. [ABSTRACT FROM AUTHOR]

Signal detection in massive MIMO systems faces many challenges. The minimum mean square error (MMSE) approach for massive multiple-input multiple-output (MIMO) communications offer near to optimal recognition but require inverting the high-dimensional matrix. To tackle this issue, a Gauss–Seidel (GS) detector based on conjugate gradient and Jacobi iteration (CJ) joint processing (CJGS) is presented. In order to accelerate algorithm convergence, the signal is first initialized using the optimal initialization regime among the three options. Second, the signal is processed via the CJ Joint Processor. The pre-processed result is then sent to the GS detector. According to simulation results, in channels with varying correlation values, the suggested iterative scheme's BER is less than that of the GS and the improved iterative scheme based on GS. Furthermore, it can approach the BER performance of the MMSE detection algorithm with fewer iterations. The suggested technique has a computational complexity of O(U2), whereas the MMSE detection algorithm has a computational complexity of O(U3), where U is the number of users. For the same detection performance, the computational complexity of the proposed algorithm is an order of magnitude lower than that of MMSE. With fewer iterations, the proposed algorithm achieves a better balance between detection performance and computational complexity. [ABSTRACT FROM AUTHOR]

We analyze the properties of the Maximum Likelihood (ML) estimator when the underlying log-likelihood function is numerically maximized with the so-called zig-zag algorithm. By splitting the parameter vector into sub-vectors, the algorithm maximizes the log-likelihood function alternatingly with respect to one sub-vector while keeping the others constant. For situations when the algorithm is initialized with a consistent estimator and is iterated sufficiently often, we establish the asymptotic equivalence of the zig-zag estimator and the "infeasible" ML estimator being numerically approximated. This result gives guidance for practical implementations. We illustrate how to employ the algorithm in different estimation problems, such as in a vine copula model and a vector autoregressive moving average model. The accuracy of the estimator is illustrated through simulations. Finally, we demonstrate the usefulness of our results in an application, where the Bitcoin heating 2017 is analyzed by a dynamic conditional correlation model. [ABSTRACT FROM AUTHOR]

Load flow (LF) analysis is one of the most important aspects in power system studies. It is the most significant and necessary way to investigate the problems in power system operation and planning. The LF problem comprises a set of nonlinear algebraic equations that must be solved mathematically through iterations. The solution convergence is the most important criteria that is largely affected by the size of power system, which continues to increase in the current modern power system field. Thus, there is no guarantee that the iterative approaches will converge to a valid solution for problems with such large dimensions. This paper develops generalized, effective and simple mathematical models for the solution of the LF problem. The problem is first solved by Gauss–Seidel (GS) method in order to generate the training data. Eureqa software is then adopted for the purpose of data training and mathematical models generation. The models relate bus voltage magnitudes and angles as output parameters with the load active and reactive power values as input parameters. To study the validity of the proposed approach, the mathematical models have been developed for two benchmark test systems; IEEE 5-bus test system and 9-bus test system developed by Western Systems Coordinating Council (WSCC). When compared with the outputs resulting from GS technique, the results have shown efficient and accurate capability of the generated models for evaluating bus voltages magnitudes and angles as well as generated reactive power. The models have also been compared with other published research. The results have shown efficient performance of the developed models. [ABSTRACT FROM AUTHOR]

The Recursive Gauss-Seidel (RGS) algorithm is presented that is implemented in a one-step Gauss-Seidel iteration for the identification of Wiener output error systems. The RGS algorithm has lower processing intensity than the popular Recursive Least Squares (RLS) algorithm due to its implementation using one-step Gauss-Seidel iteration in a sampling interval. The noise-free output samples in the data vector used for implementation of the RGS algorithm are estimated using an auxiliary model. Also, a stochastic convergence analysis is presented, and it is shown that the presented auxiliary model-based RGS algorithm gives unbiased parameter estimates even if the measurement noise is coloured. Finally, the effectiveness of the RGS algorithm is verified and compared with the equivalent RLS algorithm by computer simulations. [ABSTRACT FROM AUTHOR]

This paper introduces a conjugate gradients (CG) acceleration of the coordinate descent algorithm (CD) for linear systems. It is shown that the Kaczmarz algorithm (KACZ) can simulate CD exactly, so CD can be accelerated by CG similarly to the CG acceleration of KACZ (Björck and Elfving in BIT 19:145–163, 1979). Experimental results were carried out on large sets of problems of reconstructing bandlimited functions from random sampling. The randomness causes extreme variance between different instances of these problems, thus causing extreme variance in the advantage of CGCD over CD. The reduction of the number of iterations by CGCD varies from about 50–90% and beyond. The implementation of CGCD is simple. CGCD can also be used for the parallel solution of linear systems derived from partial differential equations, and for the efficient solution of multiple right-hand-side problems and matrix inversion. [ABSTRACT FROM AUTHOR]

Massive multiple-input multiple-output (MIMO) is an essential technology in fifth-generation (5G) and beyond 5G (B5G) communication systems. Massive MIMO is employed to meet the increasing request for high capacity in next-generation wireless communication networks. However, signal processing in massive MIMO incurs a high complexity due to a large number of transmitting and receiving antenna elements. In this paper, we propose low complexity massive MIMO data detection techniques based on zero-forcing (ZF) and vertical bell laboratories layered space-time (V-BLAST) method in combination with approximate matrix inversion techniques; Neumann series (NS) and Newton iteration (NI). The proposed techniques reduce the complexity of the ZF V-BLAST method since they avoid the exact matrix inverse computation. Initialization based on a stair matrix is also exploited to balance the performance and the complexity. In addition, we propose a massive MIMO detector based on approximate matrix inversion with a stair matrix initialization and deep learning (DL) based detector; MM Network (MMNet) algorithm. MMNet contains a linear transformation followed by a non-linear denoising stage. As signals propagate through the MMNet, the noise distribution at the input of the denoiser stages approaches a Gaussian distribution, form precisely the conditions in which the denoisers can attenuate noise maximally. We validated the performance of the proposed massive MIMO detection schemes in Gaussian and realistic channel models, i.e., Quadriga channels models. Simulations demonstrate that the proposed detectors achieve a remarkable improvement in the performance with a notable computational complexity reduction when compared to conventional ZF V-BLAST and the MMNET in both simple and real channel scenarios.

Abstract We study a “conjugate” transform on matrix spaces. For Laurent/Toeplitz operators such a transform is a way of realizing the Hilbert transform on the torus. We establish its operator norm on Schatten classes and discuss the possibility of its boundedness upon permutations. Applications in the Rademacher–Menshov inequality and iterative methods are also included.

Abstract In massive multiple-input multiple-output (MIMO) systems with single- antenna user equipment (SAUE) or multiple-antenna user equipment (MAUE), with the increase of the number of received antennas at base station, the complexity of traditional detectors is also increasing. In order to reduce the high complexity of parallel running of the traditional Gauss-Seidel iterative method, this paper proposes a model-driven deep learning detector network, namely Block Gauss-Seidel Network (BGS-Net), which is based on the Gauss-Seidel iterative method. We reduce complexity by converting a large matrix inversion to small matrix inversions. In order to improve the symbol error ratio (SER) of BGS-Net under MAUE system, we propose Improved BGS-Net. The simulation results show that, compared with the existing model-driven algorithms, BGS-Net has lower complexity and similar the detection performance; good robustness, and its performance is less affected by changes in the number of antennas; Improved BGS-Net can improve the detection performance of BGS-Net.

Stencil is a common cyclic nested computing model,which is widely used in many scientific and engineering simulation applications,such as computational electromagnetism,weather simulation,geophysics,ocean simulation and so on.With the deve-lopment of modern processor architecture,the multi-core and multi-layer memory levels have been deepened.Research on paralle-lism and locality is the main way to improve the performance of programs.Blocking is one of the main techniques to exploit data locality and program parallelism.At present,a large number of blocking methods have been proposed for Stencil,but most of them are limited to Jacobi Stencils which is featured with high parallelism and locality.Gauss-Seidel Stencil has a better convergence rate and is widely used in multi-grid calculations.However,the data dependence of this type of Stencil is more complicated.In this paper,a parallel blocking and vectorization algorithm is designed for Gauss-Seidel Stencil for red black sorting,which improves the data locality,medium granularity multi-core parallelism and intra core fine-grained parallelism of Gauss-Seidel Stencil.Experimental results demonstrate the effectiveness of this scheme.

A two-step randomized Gauss-Seidel (TRGS) method is presented for large linear least squares problem with tall and narrow coefficient matrix. The TRGS method projects the approximate solution onto the solution space by given two random columns and is proved to be convergent when the coefficient matrix is of full rank. Several numerical examples show the effectiveness of the TRGS method among all methods compared.

Signal detection in massive MIMO systems faces many challenges. The minimum mean square error (MMSE) approach for massive multiple-input multiple-output (MIMO) communications offer near to optimal recognition but require inverting the high-dimensional matrix. To tackle this issue, a Gauss–Seidel (GS) detector based on conjugate gradient and Jacobi iteration (CJ) joint processing (CJGS) is presented. In order to accelerate algorithm convergence, the signal is first initialized using the optimal initialization regime among the three options. Second, the signal is processed via the CJ Joint Processor. The pre-processed result is then sent to the GS detector. According to simulation results, in channels with varying correlation values, the suggested iterative scheme’s BER is less than that of the GS and the improved iterative scheme based on GS. Furthermore, it can approach the BER performance of the MMSE detection algorithm with fewer iterations. The suggested technique has a computational complexity of O(U2), whereas the MMSE detection algorithm has a computational complexity of O(U3), where U is the number of users. For the same detection performance, the computational complexity of the proposed algorithm is an order of magnitude lower than that of MMSE. With fewer iterations, the proposed algorithm achieves a better balance between detection performance and computational complexity.

Copyright of Técnica Industrial: Revista Cuatrimestral de Ingeniería, Industria e Innovación is the property of Fundacion Tecnica Industrial and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper presents the solution of three phases power flow in unbalanced electrical network. The main objective of the three flow analysis of power is to calculate the active and reactive powers flowing in each phase with the magnitude and the angle of the voltage at each bus of the system for the specific loading conditions. In this work, the negative- and zero-sequence components are presented using nodal voltage equations. The three phase power flow is formulated and solved by using Gauss-Seidel and Newton-Raphson methods and has been tested using IEEE 5 bus system. The wind power in this work represented by wind electric system which made up of a wind turbine mounted on a tower to provide better access to stronger winds, after that, we inject wind power generator to show the effect of the wind energy in the power flow for unbalanced electrical power system. The solar unit is considered in this work by adding two energy types in one bus. [ABSTRACT FROM AUTHOR]

We study a "conjugate" transform on matrix spaces. For Laurent/Toeplitz operators such a transform is a way of realizing the Hilbert transform on the torus. We establish its operator norm on Schatten classes and discuss the possibility of its boundedness upon permutations. Applications in the Rademacher–Menshov inequality and iterative methods are also included. [ABSTRACT FROM AUTHOR]

In massive multiple-input multiple-output (MIMO) systems with single- antenna user equipment (SAUE) or multiple-antenna user equipment (MAUE), with the increase of the number of received antennas at base station, the complexity of traditional detectors is also increasing. In order to reduce the high complexity of parallel running of the traditional Gauss-Seidel iterative method, this paper proposes a model-driven deep learning detector network, namely Block Gauss-Seidel Network (BGS-Net), which is based on the Gauss-Seidel iterative method. We reduce complexity by converting a large matrix inversion to small matrix inversions. In order to improve the symbol error ratio (SER) of BGS-Net under MAUE system, we propose Improved BGS-Net. The simulation results show that, compared with the existing model-driven algorithms, BGS-Net has lower complexity and similar the detection performance; good robustness, and its performance is less affected by changes in the number of antennas; Improved BGS-Net can improve the detection performance of BGS-Net. [ABSTRACT FROM AUTHOR]

A composite refinement technique for two stationary iterative methods, one of them contains a relaxation parameter, is introduced. Four new techniques, Jacobi successive over relaxation (SOR) composite refinement (RJSOR), SOR Jacobi composite refinement (RSORJ), Gauss–Seidel (GS) SOR composite refinement (RGSSOR) and SOR with GS composite refinement (RSORGS) are compared with their classical forms. The efficient performance of the new forms is well established and confirmed through numerical example. The computational costs and the speed of convergence are considered. The decrease in the required number of iteration is established through the calculation of the spectral radius of the iteration matrices. It is illustrated that the convergence of Jacobi and Gauss–Seidel methods engage the divergence and extend the domain of convergence in the SOR method in the refinement technique. The calculations and graphs are performed by computer algebra system, Mathematica.

A two-step randomized Gauss-Seidel (TRGS) method is presented for large linear least squares problem with tall and narrow coefficient matrix. The TRGS method projects the approximate solution onto the solution space by given two random columns and is proved to be convergent when the coefficient matrix is of full rank. Several numerical examples show the effectiveness of the TRGS method among all methods compared. [ABSTRACT FROM AUTHOR]

Focused on the issue in which the problem of low precision of channel estimation and high implementation complexity in wideband millimeter-wave(mmWave) MIMO with lens antenna array system,a successive support detection(GS-SSD) algorithm based on Gauss-Seidel method was proposed in the traditional support detection scheme.In this algorithm,the assumption of common support was not used,and inspired by the successive interference cancellation.This algorithm decomposed the total channel estimation problem into several channel component.In the meanwhile,the Gauss-Seidel method was used to approximate the matrix inversion with high complexity.Simulations were provided to show that the proposed GS-SSD algorithm could significantly reduce the complex multiplication and achieved high performance compared with successive support detection algorithm.

Membrane separation has become a panacea for various scientific and engineering problems, including water treatment, gas separation, purification, hemodialysis, and drug delivery. Modeling and simulation of such systems are necessary for the design, analysis, and optimization of membrane separation processes. Despite numerous studies, an efficient numerical solution of such systems is an open problem, especially when speed and reliability matter. In this study, a generalized numerical framework for solving cocurrent and counter-current membrane models is proposed, which hinges on a straightforward and reliable Gauss-Seidel method with successive over-relaxation. The results confirm the speed and reliability of the proposed algorithm, while it is validated by the experimental data for the separation of a mixture of CH4 and CO2, as well as a mixture of He, CO2, N2, and CH4. The permeate outlet pressure estimation error can be reduced to any value as low as ∼10−14%, while the computational time on a personal laptop is not more than 4.5 s. This algorithm can be readily implemented in various programming languages and commercial software applications.

Asynchronous methods for solving systems of linear equations have been researched since Chazan and Miranker's [1969] pioneering paper on chaotic relaxation. The underlying idea of asynchronous methods is to avoid processor idle time by allowing the processors to continue to make progress even if not all progress made by other processors has been communicated to them. Historically, the applicability of asynchronous methods for solving linear equations has been limited to certain restricted classes of matrices, such as diagonally dominant matrices. Furthermore, analysis of these methods focused on proving convergence in the limit. Comparison of the asynchronous convergence rate with its synchronous counterpart and its scaling with the number of processors have seldom been studied and are still not well understood. In this article, we propose a randomized shared-memory asynchronous method for general symmetric positive definite matrices. We rigorously analyze the convergence rate and prove that it is linear and is close to that of the method's synchronous counterpart if the processor count is not excessive relative to the size and sparsity of the matrix. We also present an algorithm for unsymmetric systems and overdetermined least-squares. Our work presents a significant improvement in the applicability of asynchronous linear solvers as well as in their convergence analysis, and suggests randomization as a key paradigm to serve as a foundation for asynchronous methods. [ABSTRACT FROM AUTHOR]

A procedure is developed for power analysis and sample size calculation for a class of complex testing problems regarding the largest binomial probability under a combination of treatments. It is shown that the asymptotic null distribution of the likelihood-ratio statistic is not parameter-free, but $\chi _{1}^{2} $ is a conservative asymptotic null distribution. A nonlinear Gauss-Seidel algorithm is proposed to uniquely determine the alternative for the power and sample size calculation given the baseline binomial probability. An example from an animal clinical trial is discussed.

The evaluation of prediction machines is an important step for a successful implementation of genomic-enabled selection in plant breeding. Computation time and predictive ability constitute key metrics to determine the methodology utilized for the consolidation of genomic prediction pipeline. This study introduces two methods designed to couple high prediction accuracy with efficient computational performance: 1) a non-MCMC method to estimate marker effects with a Laplace prior; and 2) an iterative framework that allows solving whole-genome regression within mixed models with replicated observations in a single-stage. The investigation provides insights on predictive ability and marker effect estimates. Various genomic prediction techniques are compared based on cross-validation, assessing predictions across and within family. Properties of quantitative trait loci detection and single-stage method were evaluated on simulated plot-level data from unbalanced data structures. Estimation of marker effects by the new model is compared to a genome-wide association analysis and whole-genome regression methods. The single-stage approach is compared to a GBLUP fitted via restricted maximum likelihood, and a two-stages approaches where genetic values fit a whole-genome regression. The proposed framework provided high computational efficiency, robust prediction across datasets, and accurate estimation of marker effects.

We propose a new iterative detection and decoding (IDD) algorithm for multiple-input multiple-output (MIMO) based on expectation propagation (EP) with application to massive MIMO scenarios. Two main results are presented. We first introduce EP to iteratively improve the Gaussian approximations of both the estimation of the posterior by the MIMO detector and the soft output of the channel decoder. With this novel approach, denoted by double-EP (DEP), the convergence is very much improved with a computational complexity just two times the one of the linear minimum mean square error (LMMSE) based IDD, as illustrated by the included experiments. Besides, as in the LMMSE MIMO detector, when the number of antennas increases, the computational cost of the matrix inversion operation required by the DEP becomes unaffordable. In this work we also develop approaches of DEP where the mean and the covariance matrix of the posterior are approximated by using the Gauss-Seidel and Neumann series methods, respectively. This low-complexity DEP detector has quadratic complexity in the number of antennas, as the low-complexity LMMSE techniques. Experimental results show that the new low-complexity DEP achieves the performance of the DEP as the ratio between the number of transmitting and receiving antennas decreases. [ABSTRACT FROM AUTHOR]

The initial solution of a massive multiple-input multiple-output (M-MIMO) detector for uplink (UL) is greatly influence the balance between the bit error rate (BER) performance and the computational complexity. Although the maximum likelihood (ML) detector obtains the best BER performance, it has an extremely high computational complexity. Iterative linear minimum mean square error (MMSE) detector based on the Gauss–Seidel (GS), the successive over-relaxation (SOR), and the Jacobi (JA), obtains a good performance-complexity profile when the base station (BS)-to-user-antenna-ratio (BUAR) is large. However, when the BUAR is small, the system suffers from a considerable performance loss. In this paper, a hybrid detector based on the joint GS and SOR methods is proposed where the initial solution is determined by the first iteration of GS method. Numerical results show a considerable complexity reduction and performance enhancement using the proposed GS-SOR method over all methods when the BUAR is small. [ABSTRACT FROM AUTHOR]

We consider coordinate descent methods for minimization of convex quadratic functions, in which exact line searches are performed at each iteration. (This algorithm is identical to Gauss-Seidel on the equivalent symmetric positive definite linear system.) We describe a class of convex quadratic functions for which the random permutations version of cyclic coordinate descent (RPCD) is observed to outperform the standard cyclic coordinate descent (CCD) approach on computational tests, yielding convergence behavior similar to the fully random variant (RCD). A convergence analysis is developed to explain the empirical observations. [ABSTRACT FROM AUTHOR]

Copyright of Telecommunications Science is the property of Beijing Xintong Media Co., Ltd. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Load Flow (LF) analysis is a fundamental and significant issue in electric power systems. Because of the nonlinearity of the power mismatch equations, the accuracy of the nonlinear solvers is important. In this study, a novel and efficient nonlinear solver is proposed with active applications to LF problems. The formulation of the Proposed Method (PM) and its workflow and mathematical modeling for its application in LF problems have been discussed. The performance of the PM has been validated on the IEEE 14-bus and 30-bus test systems against several existing methods. The simulation results show that the PM exhibits higher order accuracy, faster convergence characteristics, smaller number of iterations, and lesser computation times in comparison with the other benchmark methods. [ABSTRACT FROM AUTHOR]

In this paper we study a broad class of nonconvex and nonsmooth minimization problems, whose objective function is the sum of a smooth function of the entire variables and two nonsmooth functions of each variable. We adopt the framework of the proximal alternating linearized minimization (PALM), together with the inertial strategy to accelerate the convergence. Since the inertial step is performed once the x-subproblem/y-subproblem is updated, the algorithm is a Gauss–Seidel type inertial proximal alternating linearized minimization (GiPALM) algorithm. Under the assumption that the underlying functions satisfy the Kurdyka–Łojasiewicz (KL) property and some suitable conditions on the parameters, we prove that each bounded sequence generated by GiPALM globally converges to a critical point. We apply the algorithm to signal recovery, image denoising and nonnegative matrix factorization models, and compare it with PALM and the inertial proximal alternating linearized minimization. [ABSTRACT FROM AUTHOR]

Nowadays, generation and consumption points are constantly increasing in parallel with the increasing energy demand and power systems are rapidly growing. However, it is very important to plan, install and operate the power systems in a way that ensures safe, efficient and continuous operation. For this purpose, especially load flow analysis and also other analysis methods such as protection-coordination, constraints, stability, short circuit etc. are employed for power systems. In this study, the comparison of Gauss-Seidel, Newton-Raphson and Fast Decoupled methods, commonly used in load flow analysis has been made according to the number of iterations, the computation time, the total line losses and the produced and consumed active and reactive power considering different tolerance values. As the test systems, IEEE 6-, 14, 30- and 57-bus power systems have been used in the Matlab environment. In consequence of the load flow analyses conducted, the minimum number of iterations and the minimal power loss have been achieved by the Newton-Raphson method, while the power produced by generators according to load demands on the buses has been computed close to each other for all three methods.

Systems of linear equations are ubiquitous in science and engineering, and iterative methods are indispensable for the numerical treatment of such systems. When we apprehend what properties of the coefficient matrix account for the rate of convergence, we may multiply the original system by some nonsingular matrix, called a preconditioner, so that the new coefficient matrix possesses better properties. Recently, some scholars presented several preconditioners and based on numerical tests proposed some conjectures for preconditioned iterative methods. In this paper, we prove one conjecture on the preconditioned Gauss-Seidel iterative method for solving linear systems whose coefficient matrix is an M-matrix. [ABSTRACT FROM AUTHOR]

Abstract Asynchronous iterative methods for solving linear systems are gaining renewed interest due to the high cost of synchronization points in massively parallel codes. Historically, theory on asynchronous iterative methods has focused on asymptotic behavior, while the transient behavior remains poorly understood. In this paper, we study a model of the asynchronous Jacobi method without communication delays, which we call simplified asynchronous Jacobi. Simplified asynchronous Jacobi can be used to model asynchronous Jacobi implemented in shared memory or distributed memory with fast communication networks. Our analysis uses the idea of a propagation matrix , which is similar in concept to an iteration matrix. We show that simplified asynchronous Jacobi can continue to reduce the residual when some processes are slower than other processes. We also show that simplified asynchronous Jacobi can converge when synchronous Jacobi does not. We verify our analysis of simplified asynchronous Jacobi using results from asynchronous Jacobi implemented in shared and distributed memory. Highlights • We study the asynchronous Jacobi (AJ) method for solving sparse linear systems. • A model of AJ that assumes no communication delays is analyzed. • We show that AJ can reduce the residual when a process is slower than others. • We show that AJ can converge when synchronous Jacobi does not. • Results for shared and distributed memory support our analysis of AJ. [ABSTRACT FROM AUTHOR]

This paper reports the development and convergence analysis in steady-state of an effective and robust implicit finite-volume solver for compressible Euler equations on three-dimensional unstructured grids. A second-order upwind scheme (MUSCL) was employed based on Roe's approximate Flux-Difference Scheme (FDS) by using Venkatrakishnan flux limiters. The construction of the linear system for the implicit scheme was performed by applying the backward Euler on the left-hand side of the conservation equation and Newton-type linearization on the right-hand side. The Jacobian matrix that resulted from the linearization process was computed analytically using Roe flux terms. In this phase, the defect-correction technique was employed allowing effective time-dependent computations by an implicit time-integration scheme. In this approach, the flux integral on the right-hand side is computed based on a high-order of accuracy whilst the left-hand side the Jacobian is performed based on the low-order. The resulting sparse and large system of linear equations is solved by a sequential Gauss–Seidel iterative method. Simulations were performed and the developed implicit defect-correction solver was validated and verified. In addition, convergence analysis comparing the implicit solver and the explicit Runge–Kutta of 5-steps using Implicit Residual Smoothing (IRS) were performed showing the significant speed-up of the implicit solver over the explicit one. Simulations were performed for case studies to demonstrate the robustness of the developed implicit defect-correction solver in solving typical problems of aerodynamic involving transonic condition and shock wave captures for internal and external flows. Finally, the main particularities of the implicit scheme were investigated and discussed considering the simulation results, showing also its capacity to serve as an effective preconditioner (start-up method) to other implicit techniques. [ABSTRACT FROM AUTHOR]

In this paper, we propose a simple and practical preconditioner based on the homotopy analysis method. Furthermore, using this modeling, we design an efficient algorithm to solve linear systems. Within the computational framework, convection-diffusion equation candidates are investigated and evaluated. Finally, computational comparisons of the standard methods against preconditioned methods based on experiments are presented which illustrate the merits of the simplicity, power, and effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Graph convolutional networks (GCNs) have proven to be an effective approach for 3D human pose estimation. By naturally modeling the skeleton structure of the human body as a graph, GCNs are able to capture the spatial relationships between joints and learn an efficient representation of the underlying pose. However, most GCN-based methods use a shared weight matrix, making it challenging to accurately capture the different and complex relationships between joints. In this paper, we introduce an iterative graph filtering framework for 3D human pose estimation, which aims to predict the 3D joint positions given a set of 2D joint locations in images. Our approach builds upon the idea of iteratively solving graph filtering with Laplacian regularization via the Gauss–Seidel iterative method. Motivated by this iterative solution, we design a Gauss–Seidel network (GS-Net) architecture, which makes use of weight and adjacency modulation, skip connection, and a pure convolutional block with layer normalization. Adjacency modulation facilitates the learning of edges that go beyond the inherent connections of body joints, resulting in an adjusted graph structure that reflects the human skeleton, while skip connections help maintain crucial information from the input layer's initial features as the network depth increases. We evaluate our proposed model on two standard benchmark datasets, and compare it with a comprehensive set of strong baseline methods for 3D human pose estimation. Our experimental results demonstrate that our approach outperforms the baseline methods on both datasets, achieving state-of-the-art performance. Furthermore, we conduct ablation studies to analyze the contributions of different components of our model architecture and show that the skip connection and adjacency modulation help improve the model performance. [ABSTRACT FROM AUTHOR]

We consider a large-scale minimization problem (not necessarily convex) with non-smooth separable convex penalty. Problems in this form widely arise in many modern large-scale machine learning and signal processing applications. In this paper, we present a new perspective towards the parallel Block Coordinate Descent (BCD) methods. Specifically we explicitly give a concept of so-called two-layered block variable updating loop for parallel BCD methods in modern computing environment comprised of multiple distributed computing nodes. The outer loop refers to the block variable updating assigned to distributed nodes, and the inner loop involves the updating step inside each node. Each loop allows to adopt either Jacobi or Gauss–Seidel update rule. In particular, we give detailed theoretical convergence analysis to two practical schemes: Jacobi/Gauss–Seidel and Gauss–Seidel/Jacobi that embodies two algorithms respectively. Our new perspective and behind theoretical results help devise parallel BCD algorithms in a principled fashion, which in turn lend them a flexible implementation for BCD methods suited to the parallel computing environment. The effectiveness of the algorithm framework is verified on the benchmark tasks of large-scale ℓ 1 regularized sparse logistic regression and non-negative matrix factorization. [ABSTRACT FROM AUTHOR]

Stochastic iterative algorithms such as the Kaczmarz and Gauss–Seidel methods have gained recent attention because of their speed, simplicity, and the ability to approximately solve large-scale linear systems of equations without needing to access the entire matrix. In this work, we consider the setting where we wish to solve a linear system in a large matrix X that is stored in a factorized form, X = UV ; this setting either arises naturally in many applications or may be imposed when working with large low-rank datasets for reasons of space required for storage. We propose a variant of the randomized Kaczmarz method for such systems that takes advantage of the factored form and avoids computing X. We prove an exponential convergence rate and supplement our theoretical guarantees with experimental evidence demonstrating that the factored variant yields significant acceleration in convergence. [ABSTRACT FROM AUTHOR]

The main objective of this research was to study the suspension of particles in a turbulent flow (k-ε model) of a Newtonian fluid between two rigid walls. The mathematical study is presented by Navier-Stokes equations and equation of transport of the particles. In order to study the effect of the fluctuations, the decomposition of Reynolds was applied to all the equations previously established. The approach of the phenomenon is made using mathematical and numerical way by using the finite volume method as a method of discretization, and the Gauss-Seidel method as a method of solution. This is to establish a numerical code, using the FORTRAN language, which makes it possible to solve the equations and to determine the particle's concentration profile c, and the fluid velocities u, w respectively in Cartesian coordinate. The work carried out concerns the understanding and the modeling of the mechanisms of suspension of solid particles in a fluid flow. [ABSTRACT FROM AUTHOR]

The Kaczmarz and Gauss-Seidel methods aim to solve an m x n linear system Xβ = y by iteratively refining the solution estimate; the former uses random rows of X to update β given the corresponding equations and the latter uses random columns of X to update corresponding coordinates in β. Recent work analyzed these algorithms in a parallel comparison for the overcomplete and undercomplete systems, showing convergence to the ordinary least squares (OLS) solution and the minimum Euclidean norm solution, respectively. This paper considers the natural follow-up to the OLS problem--ridge or Tikhonov regularized regression. By viewing them as variants of randomized coordinate descent, we present variants of the randomized Kaczmarz (RK) and randomized Gauss-Siedel (RGS) for solving this system and derive their convergence rates. We prove that a recent proposal, which can be interpreted as randomizing over both rows and columns, is strictly suboptimal--instead, one should always work with randomly selected columns (RGS) when m > n (#rows > #cols) and with randomly selected rows (RK) when n > m (#cols > #rows). [ABSTRACT FROM AUTHOR]

This paper studies the ℓ q ( 0 < q < 1 ) regularized least squares regression ( ℓ q LS) problem, which arises in many applications of signal processing and machine learning. The iterative thresholding algorithm is an important algorithm for solving the ℓ q LS problem, and can be viewed as a Jacobi-type iterative method. This paper proposes a Gauss–Seidel version of iterative thresholding algorithm called GAITA for solving the ℓ q LS problem. Under certain conditions, we establish its global convergence 1 1 The global convergence in this paper is defined in the sense that the entire sequence converges regardless of the initial point. , eventual linear rate, and the convergence to a local minimizer. Compared to the Jacobi counterpart, the proposed algorithm can allow larger step sizes and converge much faster. The effectiveness of the proposed algorithm is justified with numerical experiments on both synthetic data and real data. [ABSTRACT FROM AUTHOR]

The MPACT code, being developed collaboratively by the University of Michigan and Oak Ridge National Laboratory, is the primary deterministic neutron transport solver being deployed within the Virtual Environment for Reactor Applications (VERA) as part of the Consortium for Advanced Simulation of Light Water Reactors (CASL). In many applications of the MPACT code, transport-corrected scattering has proven to be an obstacle in terms of stability, and considerable effort has been made to try to resolve the convergence issues that arise from it. Most of the convergence problems seem related to the transport-corrected cross sections, particularly when used in the 2D method of characteristics (MOC) solver, which is the focus of this work. In this paper, the stability and performance of the 2-D MOC solver in MPACT is evaluated for two iteration schemes: Gauss-Seidel and Jacobi. With the Gauss-Seidel approach, as the MOC solver loops over groups, it uses the flux solution from the previous group to construct the inscatter source for the next group. Alternatively, the Jacobi approach uses only the fluxes from the previous outer iteration to determine the inscatter source for each group. Consequently for the Jacobi iteration, the loop over groups can be moved from the outermost loop—as is the case with the Gauss-Seidel sweeper—to the innermost loop, allowing for a substantial increase in efficiency by minimizing the overhead of retrieving segment, region, and surface index information from the ray tracing data. Several test problems are assessed: (1) Babcock & Wilcox 1810 Core I, (2) Dimple S01A-Sq, (3) VERA Progression Problem 5a, and (4) VERA Problem 2a. The Jacobi iteration exhibits better stability than Gauss-Seidel, allowing for converged solutions to be obtained over a much wider range of iteration control parameters. Additionally, the MOC solve time with the Jacobi approach is roughly 2.0–2.5× faster per sweep. While the performance and stability of the Jacobi iteration are substantially improved compared to the Gauss-Seidel iteration, it does yield a roughly 8–10% increase in the overall memory requirement. [ABSTRACT FROM AUTHOR]

Iterative algorithms are frequently used to resolve simultaneous impacts between rigid bodies in physical simulations. However, these algorithms lack formal guarantees of termination, which is sometimes viewed as potentially dangerous, so failsafes are used in practical codes to prevent infinite loops. We show such steps are unnecessary. In particular, we study the broad class of such algorithms that are conservative and satisfy a minimal set of physical correctness properties, and which encompasses recent methods like Generalized Reflections as well as pairwise schemes. We fully characterize finite termination of these algorithms. The only possible failure cases can be detected, and we describe a procedure for modifying the algorithms to provably ensure termination. We also describe modifications necessary to guarantee termination in the presence of numerical error due to the use of floating-point arithmetic. Finally, we discuss the challenges dissipation introduce for finite termination, and describe how dissipation models can be incorporated while retaining the termination guarantee. [ABSTRACT FROM AUTHOR]