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In this paper, a new real representation of reduced biquaternion matrix is proposed, and the solutions of the reduced biquaternion matrix equations XF−AX=BY$$ XF- AX= BY $$ and XF−AX˜=BY$$ XF-A\tilde{X}= BY $$ are solved by means of this method. The corresponding numerical algorithm is provided, and the effectiveness of this method is verified by numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, the problem of clustering data points that lie near or on a union of independent low‐dimensional subspaces is addressed. To this end, the popular spectral clustering‐based algorithms usually follow a two‐stage strategy that initially builds an affinity matrix and then applies spectral clustering. However, an inappropriate affinity matrix that does not sufficiently connect data points lying on the same subspace will easily lead to the issue of over‐segmentation. To alleviate this issue, building the affinity matrix based on subspace hypotheses generated by an iterative sampling operation according to the Random Cluster Model under the framework of energy minimisation is proposed. Specifically, each hypothesis is generated from a large number of data points by sampling a component in a K‐nearest neighbour graph. Extensive experiments on synthetic data and real‐world datasets show that the proposed method can improve the connectivity of the affinity matrix and provide competitive results against state‐of‐the‐art methods. [ABSTRACT FROM AUTHOR]

Summary: Most of networks in real world obviously present dynamic characteristics over time, and the community structure of adjacent snapshots has a certain degree of instability and temporal smoothing. Traditional Temporal Trade‐off algorithms consider that communities found at time t depend both on past evolutions. Because this kind of algorithms are based on the hypothesis of short‐term smoothness, they can barely find abnormal evolution and group emergence in time. In this paper, a Dynamic Community Detection method based on an improved Evolutionary Matrix (DCDEM) is proposed, and the improved evolutionary matrix combines the community structure detected at the previous time with current network structure to track the evolution. Firstly, the evolutionary matrix transforms original unweighted network into weighted network by incorporating community structure detected at the previous time with current network topology. Secondly, the Overlapping Community Detection based on Edge Density Clustering with New edge Similarity (OCDEDC_NS) algorithm is applied to the evolutionary matrix in order to get edge communities. Thirdly, some small communities are merged to optimize the community structure. Finally, the edge communities are restored to the node overlapping communities. Experiments on both synthetic and real‐world networks demonstrate that the proposed algorithm can detect evolutionary community structure in dynamic networks effectively. [ABSTRACT FROM AUTHOR]

Sorted QR decomposition (SQRD) has been extensively adopted for various multiple‐input‐multiple‐output (MIMO) detectors, in which the sorting process incurs severe latency when it comes to larger‐scale MIMO situations. This paper proposes a group‐SQRD (GSQRD) algorithm to alleviate the latency problem of general SQRD architectures for larger‐scale MIMO systems. Via predictively sorting a group of 4 columns at one stage, the GSQRD could eliminate the processing latency by 41% for decomposing 16×16 complex‐valued matrices. Additionally, this percentage even rises up to 68% for decomposing 128×128 matrices. To analyse the side effects, the GSQRD is applied in various MIMO detectors in a simulation link, which exhibits a negligible performance degradation for MIMO detection. Moreover, GSQRD is a hardware‐friendly algorithm because the division and square root operations in GSQRD are converted to multiplications for simplifying the hardware implementation. Based on this algorithm, two corresponding hardware architectures, which contains 2 and 4 columns respectively in a sorting group, are also implemented with 65‐nm CMOS technology. These architectures can work at 513 MHz to decompose 16×16 complex‐valued matrices. The processing latencies are respectively 0.32 and 0.26 μs, superior to the state‐of‐art designs. [ABSTRACT FROM AUTHOR]

This paper explores the issue of state estimation for Boolean control networks (BCNs), and a kind of improved multiple‐state observer is proposed. The improved multiple‐state observer can be described by means of a specific BCN that overcomes the difficulty of the existing multiple state observers where it is difficult to find a general expression for the observer gain matrix. Next, based on the states that can possibly generate the output and those that are observed by the designed observer in current time step, an adaptive algorithm that completes the design of the multiple‐state observer is provided to update the observer states, and which makes the state estimation of Boolean control networks feasible. Finally, an example is presented to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

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In this paper, we present frequency‐weighted optimal Hankel‐norm model reduction algorithms for linear time‐invariant continuous‐time systems by representing an original higher‐order system into new fictitious systems. The new system representations are derived through factorization of the resulting sub‐matrices that are obtained after transformations. As the proposed approaches are factorization dependent, additional results with both approaches are included using another factorization of the fictitious input–output and weight matrices. The proposed algorithms generate stable reduced models with double‐sided weights and provide a substantial improvement in the weighted error. A numerical example is given to compare the efficacy of the proposed algorithms with the well‐known frequency‐weighted techniques. [ABSTRACT FROM AUTHOR]

Consider a nondifferentiable complex fractional programming $$ {\rm minimize} \, { {\rm Re} [ f(z, {\bar z}) + (z ^{H}Az) ^{1/2} ] \over {\rm Re} [ g(z, {\bar z}) - (z ^{H}Bz)^{1/2}} \qquad {\rm subject \, to} \, h(z, {\bar z}) \in S \subset C^{m}, \quad z \in C^{m}, \leqno (2) $$ where f, g : C2n → C and h : C2n → Cm are analytic functions, A, B ∈ Cn × n are positive semidefinite Hermitian matrices, S is a polyhedral cone in Cm. In this paper, we establish conditions for the existence of an optimal solution in (P) involving (ℒ, ρ, θ)-quasiconvex/-pseudoconvex analytic functions. Based on the sufficient optimality theorem, we construct a duality model and then establish weak/strong, and strict converse duality theorems. [ABSTRACT FROM AUTHOR]

Abstract: There are important relationships between the discrete‐time linear periodic descriptor systems and the discrete‐time periodic matrix equations. In the present paper, we introduce the matrix form of the biconjugate residual (BCR) algorithm for solving the discrete‐time periodic Sylvester matrix equations AiXiBi+CiXi+1Di=Ei,i=1,2,.... It is shown that the introduced algorithm converges to the solutions within a finite number of iterations in the absence of round‐off errors. Finally, three numerical examples are given to demonstrate the efficiency and the performance of the algorithm. [ABSTRACT FROM AUTHOR]

The inverse eigenvalue problem appears repeatedly in a variety of applications. The aim of this paper is to study a quadratic inverse eigenvalue problem of the form AXΛ2 + BXΛ + CX = 0 where A, B and C should be partially bisymmetric under a prescribed submatrix constraint. We derive an efficient matrix method based on the Hestenes‐Stiefel (HS) version of biconjugate residual (BCR) algorithm for solving this constrained quadratic inverse eigenvalue problem. The theoretical results demonstrate that the matrix method solves the constrained quadratic inverse eigenvalue problem within a finite number of iterations in the absence of round‐off errors. Finally we validate the accuracy and efficiency of the matrix method through the numerical results. [ABSTRACT FROM AUTHOR]

This paper is a comparative analysis of two prominent iterative algorithms for model order reduction of linear time‐varying (LTV) periodic systems where the system's matrices are singular. Our proposed method is based on a reformulation of the LTV model to an equivalent linear time‐invariant (LTI) model using a suitable discretization procedure. The resulting LTI model is reduced in two ways, once by applying a balanced truncation method and once by applying a Krylov‐based method known as iterative rational Krylov algorithm (IRKA). During the application of balanced truncation, the low‐rank Cholesky factorized alternating directions implicit (LRCF‐ADI) method is used to estimate the solutions of the corresponding LTI form of Lyapunov equations. Since the system's matrices are singular, the concept of pseudo‐inverse is adopted to compute the shift parameters needed in the LRCF‐ADI iterations. For the Krylov‐based IRKA, our work is twofold. We solve the time‐invariant Lyapunov equation for the observability Gramian and apply a moment‐matching Krylov technique. The accuracy and effectiveness of the two proposed techniques are demonstrated with the help of frequency response graphs, bode plots, and eigenstructure of the main and reduced models. [ABSTRACT FROM AUTHOR]

An interference leakage minimisation transceiver design for multiple‐input multiple‐output Interference Channel networks is proposed by making use of the full rank constraint of the desired signal, the low rank constraint and low power constraint of the interference signal. The objective is to suppress interference leakage caused by not only the signal from other users, but also the other streams from the same user. To do so, the transmit precoding matrix and the receive filtering matrix are iteratively optimised through convex optimisation tools at stream level. Furthermore, a Min–Max interference leakage algorithm is also proposed to suppress the maximum interference from user, with the purpose of guaranteeing the fairness among users. Simulation results demonstrate that taking inter‐stream interference into consideration can significantly improve the effectiveness of multiple‐input multiple‐output Interference Channel networks, while the Min–Max method can slightly increase the system capacity under certain conditions. It can be also confirmed that the trade‐off among effectiveness, fairness and robustness exists in the transceiver optimisation of multiple‐input multiple‐output Interference Channel networks. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a new approach to multicriteria decision analysis. They were named as processing technique of ratings for ranking of alternatives (PROTERRA). The consecutive steps of the process include normalization of the ratings, calculating of the ratings ratios within each pair of the alternatives, creating a component matrix for each of the criteria, and creating a total matrix that is the sum of the weighted component matrices. Aggregated ratings of individual alternatives result from the sums of all the values of the corresponding rows and columns of the total matrix elements. A practical application of the PROTERRA has been illustrated with an example of a decision problem concerning the choice of a shopping centre location. The analysis results of the PROTERRA are compared with other results obtained using the most popular methods, that is, analytic hierarchy process, preference ranking organization method for enrichment of evaluations, and technique for order performance by similarity to ideal solution. In order to assess the stability of the ranking order obtained by the PROTERRA algorithm, the influence of weights variations on the final ranking results were tested. The sensitivity analysis was also carried out for the other methods, that is, preference ranking organization method for enrichment of evaluations, analytic hierarchy process, and technique for order performance by similarity to ideal solution. On this basis, a stability of rankings resulting from all analysed methods were compared. [ABSTRACT FROM AUTHOR]

In the present paper, we describe an adaptive modified rational global Lanczos algorithm for model-order reduction problems using multipoint moment matching-based methods. The major problem of these methods is the selection of some interpolation points. We first propose a modified rational global Lanczos process and then we derive Lanczos-like equations for the global case. Next, we propose adaptive techniques for choosing the interpolation points. Second-order dynamical systems are also considered in this paper, and the adaptive modified rational global Lanczos algorithm is applied to an equivalent state space model. Finally, some numerical examples will be given. [ABSTRACT FROM AUTHOR]

Summary: This article presents a fast sequential algorithm for the matrix chain ordering problem. Our solution is based on Yao's sequential algorithm that solves this problem in 𝒪(n2) time by reducing the total number of distinct subproblems to be performed. We solve them fastly by avoiding some unnecessary computations. Our strategy consists in organizing the evaluation of the subproblems according to their dependencies instead of their precedence order as in the previous solutions. In many cases, our solution runs in 𝒪(n) time. An experimental study is conducted to benchmark the performance of our algorithm by measuring the average of the results obtained on five random data sets. This shows that our algorithm is ×18.93 faster than Yao's sequential algorithm and ×5.07 faster than the previous best CGM‐based parallel solutions on 32 processors. [ABSTRACT FROM AUTHOR]

In this paper, the problem of finite-time H ∞ control is addressed for a class of discrete-time switched nonlinear systems with time delay. The concept of H ∞ finite-time boundedness is first introduced for discrete-time switched delay systems. Next, a set of switching signals are designed by using the average dwell time approach, under which some delay-dependent sufficient conditions are derived to guarantee the H ∞ finite-time boundedness of the closed-loop system. Then, a finite-time H ∞ state feedback controller is also designed by solving such conditions. Furthermore, the problem of uniform finite-time H ∞ stabilization is also resolved. All the conditions are cast into linear matrix inequalities, which can be easily checked by using recently developed algorithms for solving linear matrix inequalities. A numerical example and a water-quality control system are provided to demonstrate the effectiveness of the main results. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with the complete parametric solutions to the generalized discrete Yakubovich-transpose matrix equation X − AXTB = CY. which is related with several types of matrix equations in control theory. One of the parametric solutions has a neat and elegant form in terms of the Krylov matrix, a block Hankel matrix and an observability matrix. In addition, the special case of the generalized discrete Yakubovich-transpose matrix equation, which is called the Karm- Yakubovich-transpose matrix equation, is considered. The explicit solutions to the Karm- Yakubovich-transpose matrix equation are also presented by the so-called generalized Leverrier algorithm. At the end of the paper, two examples are given to show the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

We propose a novel regularized mixture model for clustering matrix‐valued data. The proposed method assumes a separable covariance structure for each cluster and imposes a sparsity structure (eg, low rankness, spatial sparsity) for the mean signal of each cluster. We formulate the problem as a finite mixture model of matrix‐normal distributions with regularization terms, and then develop an expectation maximization type of algorithm for efficient computation. In theory, we show that the proposed estimators are strongly consistent for various choices of penalty functions. Simulation and two applications on brain signal studies confirm the excellent performance of the proposed method including a better prediction accuracy than the competitors and the scientific interpretability of the solution. [ABSTRACT FROM AUTHOR]

Based on the spectral divide‐and‐conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3):A1325–A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix with small bandwidth, with the eigenvectors given implicitly as a product of orthonormal matrices stored in the so‐called hierarchically off‐diagonal low‐rank (HODLR) format. For this purpose, we combine our previous work on the fast computation of spectral projectors in the HODLR format, with a novel technique for extracting a basis for the range of such a HODLR matrix. Preliminary numerical experiments demonstrate that our algorithm exhibits quasi‐linear complexity for matrices that can be efficiently represented in the HODLR format throughout the divide‐and‐conquer algorithm, and allows for conveniently dealing with such large‐scale matrices. [ABSTRACT FROM AUTHOR]

We introduce a novel parametrization of the correlation matrix. The reparametrization facilitates modeling of correlation and covariance matrices by an unrestricted vector, where positive definiteness is an innate property. This parametrization can be viewed as a generalization of Fisher's Z‐transformation to higher dimensions and has a wide range of potential applications. An algorithm for reconstructing the unique n × n correlation matrix from any vector in Rn(n−1)/2 is provided, and we derive its numerical complexity. [ABSTRACT FROM AUTHOR]

The study addresses the consensus problem of linear time invariant (LTI) multi-agent systems with constant input delay and matched external disturbances by using relative output information. First, distributed disturbance observers are constructed to estimate the disturbances generated by linear exosystems with unknown initial conditions. Next, a disturbance observer-based predictor feedback control law is developed for each agent to realise consensus disturbance rejection in the presence of input delay. Then, a linear matrix inequality-based control design algorithm is given to determine the satisfactory control parameters. It is proved that state consensus can be achieved for both leaderless and leader--follower networks in the presence of large input delay and matched disturbances under the control scheme. Finally, a simulation example is provided to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, two accelerated divide-and-conquer (ADC) algorithms are proposed for the symmetric tridiagonal eigenvalue problem, which cost O(N2r) flops in the worst case, where N is the dimension of the matrix and r is a modest number depending on the distribution of eigenvalues. Both of these algorithms use hierarchically semiseparable (HSS) matrices to approximate some intermediate eigenvector matrices, which are Cauchy-like matrices and are off-diagonally low-rank. The difference of these two versions lies in using different HSS construction algorithms, one (denoted by ADC1) uses a structured low-rank approximation method and the other (ADC2) uses a randomized HSS construction algorithm. For the ADC2 algorithm, a method is proposed to estimate the off-diagonal rank. Numerous experiments have been carried out to show their stability and efficiency. These algorithms are implemented in parallel in a shared memory environment, and some parallel implementation details are included. Comparing the ADCs with highly optimized multithreaded libraries such as Intel MKL, we find that ADCs could be more than six times faster for some large matrices with few deflations. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, a propagator matrix method applied to logging-while-drilling tools is introduced and extended to deal with the anisotropic and radially inhomogeneous earth formations. This method expands the Maxwell's equations in the transverse direction, constructs the relationship between propagator matrix and reflection matrix, and obtains the solution by using the reflection matrix. We systematically derived the formulas of propagator matrix method in isotropic media, uniaxially anisotropic media, fully anisotropic media, and radially inhomogeneous media respectively. In order to obtain the propagator matrix in complex media, we used the fourth-order Runge-Kutta scheme. Numerical experiments show that, compared with traditional methods, the propagator matrix method has wide range of applications while maintaining low computational costs and high accuracy. All algorithms presented in the paper have been parallelized and implemented on a high-performance computing platform. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with the tight enclosure of matrix multiplication AB for two floating-point matrices A and B. The aim of this paper is to compute component-wise upper and lower bounds of the exact result C of the matrix multiplication AB by floating-point arithmetic. Namely, an interval matrix enclosing C is obtained. In this paper, new algorithms for enclosing C are proposed. The proposed algorithms are designed to mainly exploit the level 3 operations in BLAS. Although the proposed algorithms take around twice as much costs as a standard algorithm promoted by Oishi and Rump, the accuracy of the result by the proposed algorithms is better than that of the standard algorithm. At the end of this paper, we present numerical examples showing the efficiency of the proposed algorithms. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, a rapid iterative algorithm is proposed to find robust approximations for the inverse of nonsingular matrices. The analysis of convergence reveals that this high-order method possesses eighth-order convergence. The interesting point is that, this rate is attained using less number of matrix-by-matrix multiplications in contrast to the existing methods of the same type in the literature. The extension of the method for finding Moore-Penrose inverse of singular or rectangular matrices is also presented. Numerical comparisons will be given to show the applicability, stability and consistency of the new scheme by paying special attention on the computational time. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a realization of an arbitrary conductance matrix using operational amplifiers, together with same applications. It is shown first that any conductance matrix can be realized using operational amplifiers, and the design algorithm which is convenient in the realization is given in the form of a flowchart. Then as an application, a construction of a practical matched bilateral amplifier is presented, together with its application. The realization of a gyrator is also shown. The method presented in this paper is a new and simple way to realize an arbitrary conductance matrix. The matched bilateral amplifier obtained by the proposed method is simple and better than the traditional circuit in terms of the number of circuit elements, element sensitivity, adjustment of the matching impedance, dynamic range and stability. As a practical example of application, the circuit is applied to the four-line carrier telephone link. [ABSTRACT FROM AUTHOR]

Summary: Following the Perron theorem, the spectral radius of a primitive matrix is a simple eigenvalue. It is shown that for a primitive matrix A, there is a positive rank one matrix X such that B = A ∘ X, where ∘ denotes the Hadamard product of matrices, and such that the row (column) sums of matrix B are the same and equal to the Perron root. An iterative algorithm is presented to obtain matrix B without an explicit knowledge of X. The convergence rate of this algorithm is similar to that of the power method but it uses less computational load. A byproduct of the proposed algorithm is a new method for calculating the first eigenvector. [ABSTRACT FROM AUTHOR]

The reconstruction algorithm is one of the core issues in applying compressed sensing theory to practical applications. Two-dimensional orthogonal matching pursuit (2DOMP) algorithm, as an extension of the traditional orthogonal matching pursuit algorithm, can be used directly for the reconstruction of two-dimensional signals. With 2D separable sampling, the memory requirements and the complexity of 2DOMP are exponentially reduced. However, in 2DOMP algorithm, the requirement of reconstruction matrix is not taken into consideration, merely measurement matrix is used directly. In this study, singular value decomposition is introduced into 2DOMP algorithm, and 2DOMP algorithm based on singular value decomposition (2DOMP-SVD) is proposed. Singular value decomposition of separable measurement matrices is used to obtain optimised separable reconstruction matrices and optimised measurements. Numerical experiments demonstrate that the proposed 2DOMP-SVD algorithm can significantly improve the success rate and robustness of reconstruction. Moreover, the separation design of the matrix can satisfy the requirements for both the measurement matrix and the reconstruction matrix individually, and is suitable for general separable linear system. [ABSTRACT FROM AUTHOR]

Summary: We present the augmented matrix for principal submatrix update (AMPS) algorithm, a finite element solution method that combines principal submatrix updates and Schur complement techniques, well‐suited for interactive simulations of deformation and cutting of finite element meshes. Our approach features real‐time solutions to the updated stiffness matrix systems to account for interactive changes in mesh connectivity and boundary conditions. Updates are accomplished by an augmented matrix formulation of the stiffness equations to maintain its consistency with changes to the underlying model without refactorization at each timestep. As changes accumulate over multiple simulation timesteps, the augmented solution algorithm enables tens or hundreds of updates per second. Acceleration schemes that exploit sparsity, memoization and parallelization lead to the updates being computed in real time. The complexity analysis and experimental results for this method demonstrate that it scales linearly with the number of nonzeros of the factors of the stiffness matrix. Results for cutting and deformation of three‐dimensional (3D) elastic models are reported for meshes with up to 50 000 nodes, and involve models of surgery for astigmatism and the brain. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of weakly nonlinear complementarity problems arising from the discretization of free boundary problems. By reformulating the complementarity problems as implicit fixed-point equations based on splitting of the system matrices, we propose a class of modulus-based matrix splitting algorithms. We show their convergence by assuming that the system matrix is positive definite. Moreover, we give several kinds of typical practical choices of the modulus-based matrix splitting iteration methods based on the different splitting of the system matrix. Numerical experiments on two model problems are presented to illustrate the theoretical results and examine the numerical effectiveness of our modulus-based matrix splitting algorithms. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Among numerous iterative methods for solving the minimal nonnegative solution of an M-matrix algebraic Riccati equation, the structure-preserving doubling algorithm (SDA) stands out owing to its overall efficiency as well as accuracy. SDA is globally convergent and its convergence is quadratic, except for the critical case for which it converges linearly with the linear rate 1/2. In this paper, we first undertake a delineatory convergence analysis that reveals that the approximations by SDA can be decomposed into two components: the stable component that converges quadratically and the rank-one component that converges linearly with the linear rate 1/2. Our analysis also shows that as soon as the stable component is fully converged, the rank-one component can be accurately recovered. We then propose an efficient hybrid method, called the two-phase SDA, for which the SDA iteration is stopped as soon as it is determined that the stable component is fully converged. Therefore, this two-phase SDA saves those SDA iterative steps that previously have to have for the rank-one component to be computed accurately, and thus essentially, it can be regarded as a quadratically convergent method. Numerical results confirm our analysis and demonstrate the efficiency of the new two-phase SDA. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A return mapping algorithm in principal stress space for unified strength theory (UST) model is presented in this paper. In contrast to Mohr-Coulomb and Tresca models, UST model contains two planes and three corners in the sextant of principal stress space, and the apex is formed by the intersection of 12 corners rather than the six corners of Mohr-Coulomb in the whole principal stress space. In order to utilize UST model, the existing return mapping algorithm in principal stress space is modified. The return mapping schemes for one plane, middle corner, and apex of UST model are derived, and corresponding consistent constitutive matrices in principal stress space are constructed. Because of the flexibility of UST, the present model is not only suitable for analysis based on the traditional yield functions, such as Mohr-Coulomb, Tresca, and Mises, but might also be used for analysis based on a series of new failure criteria. The accuracy of the present model is assessed by the iso-error maps. Three numerical examples are also given to demonstrate the capability of the present algorithm. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, finite-time stability and stabilization problems for a class of linear stochastic systems are studied. First, a new concept of finite-time stochastic stability is defined for linear stochastic systems. Then, based on matrix inequalities, some sufficient conditions under which the stochastic systems are finite-time stochastically stable are given. Subsequently, the finite-time stochastic stabilization is studied and some sufficient conditions for the existence of a state feedback controller and a dynamic output feedback controller are presented by using a matrix inequality approach. An algorithm is given for solving the matrix inequalities arising from finite-time stochastic stability (stabilization). Finally, two examples are employed to illustrate the results. [ABSTRACT FROM AUTHOR]

ABSTRACT In this paper, we derive a GPS/INS integration algorithm based on the direction cosine matrix (DCM) attitude representation model and analyze its performance. The motivation for this work is to find an algorithm that is capable of tracking the variation of the gyro bias vector during operations and that benefits from the established DCM based attitude estimation algorithms. Filter performance is evaluated using a simulation based on an air vehicle trajectory profile and is compared with an Euler angles-based unscented Kalman filter (UKF). We investigate the effects of improper initialization of the state vector on the filter performance. These results are supplemented using experimental data collected along a car route with two different grades of inertial measurement units (IMUs). The DCM based model has some advantages over other attitude representations due to its relatively moderate computational load and applicability with different categories of inertial sensors. Copyright © 2012 Institute of Navigation [ABSTRACT FROM AUTHOR]

Beautiful formulas are knownfor the expected cost of random two-dimensional assignment problems, but in higher dimensions even the scaling is not known. In three dimensions and above, the problem has natural "Axial" and "Planar" versions, both of which are NP-hard. For 3-dimensional Axial random assignment instances of size n, the cost scales as Ω(1/n), and a main result of the present paper is a linear-time algorithm that, with high probability, finds a solution of cost O(n-1+o(1)). For 3- dimensional Planar assignment, the lower bound is Ω(n), and we give a new efficient matching-based algorithm that with high probability returns a solution with cost O(n log n). [ABSTRACT FROM AUTHOR]

SUMMARY Novel memory-efficient Arnoldi algorithms for solving matrix polynomial eigenvalue problems are presented. More specifically, we consider the case of matrix polynomials expressed in the Chebyshev basis, which is often numerically more appropriate than the standard monomial basis for a larger degree d. The standard way of solving polynomial eigenvalue problems proceeds by linearization, which increases the problem size by a factor d. Consequently, the memory requirements of Krylov subspace methods applied to the linearization grow by this factor. In this paper, we develop two variants of the Arnoldi method that build the Krylov subspace basis implicitly, in a way that only vectors of length equal to the size of the original problem need to be stored. The proposed variants are generalizations of the so-called quadratic Arnoldi method and two-level orthogonal Arnoldi procedure methods, which have been developed for the monomial case. We also show how the typical ingredients of a full implementation of the Arnoldi method, including shift-and-invert and restarting, can be incorporated. Numerical experiments are presented for matrix polynomials up to degree 30 arising from the interpolation of nonlinear eigenvalue problems, which stem from boundary element discretizations of PDE eigenvalue problems. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY The aim of the nuclear norm minimization problem is to find a matrix that minimizes the sum of its singular values and satisfies some constraints simultaneously. Such a problem has received more attention largely because it is closely related to the affine rank minimization problem, which appears in many control applications including controller design, realization theory, and model reduction. In this paper, we first propose an exact version alternating direction method for solving the nuclear norm minimization problem with linear equality constraints. At each iteration, the method involves a singular value thresholding and linear matrix equations which are solved exactly. Convergence of the proposed algorithm is followed directly. To broaden the capacity of solving larger problems, we solve approximately the subproblem by an iterative method with the Barzilai-Borwein steplength. Some extensions to the noisy problems and nuclear norm regularized least-square problems are also discussed. Numerical experiments and comparisons with the state-of-the-art method FPCA show that the proposed method is effective and promising. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, we revisit the steady-state solution method for Markov Regenerative Processes (MRP) proposed in the work by German. This method solves the embedded Markov chain P of the MRP without storing the matrix P explicitly. We address three issues left open in German's Work: 1) the solution method is restricted to Power method; 2) it has been defined only for ergodic MRPs; and 3) no preconditioning is available to speed-up the computation. This paper discusses how to lift these limitations by extending the algorithm to preconditioned Krylov-subspace methods and by generalizing it to the non-ergodic case. An MRP-specific preconditioner is also proposed, which is built from a sparse approximation of the MRP matrix, computed via simulation. An experimental assessment of the proposed preconditioner is then provided. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The article presents a study which explained shrunk multiline addressing method (SMLA) in a passive-matrix driven liquid powder display. The researchers devised an algorithm to collect SMLA data that quickly reduces the number of scanning lines. The update time is said to be reduced by 44.5% and remained the same regardless of the increase in image size. Results confirmed reduction in the update time with the same image quality as that of the conventional ones.

This paper is motivated by some recent work of Fukuda, Ishiwata, Iwasaki, and Nakamura ( Inverse Problems 2009; :015007). We first design an algorithm for computing the eigenvalues of a specially structured matrix from the discrete Bogoyavlensky Lattice 2 (dBL2) system. A Lax representation for the dBL2 system is given in a matrix form. By considering the asymptotic behavior of dBL2 variables, some characteristic polynomials are then factorized. A new algorithm for computing the complex eigenvalues of a specially structured matrix is then introduced. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper concerns the LBM factorization of unsymmetric tridiagonal matrices, where L and M are unit lower triangular matrices and B is block diagonal with 1×1 and 2×2 blocks. In some applications, it is necessary to form this factorization without row or column interchanges while the tridiagonal matrix is formed. Bunch and Kaufman proposed a pivoting strategy without interchanges specifically for symmetric tridiagonal matrices, and more recently, Bunch and Marcia proposed pivoting strategies that are normwise backward stable for linear systems involving such matrices. In this paper, we extend these strategies to the unsymmetric tridiagonal case and demonstrate that the proposed methods both exhibit bounded growth factors and are normwise backward stable. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Some computational issues related to the identification of modal parameters of structures are presented in this paper. Optimal estimation of modal parameters often requires the solution of an overdetermined linear system of equations. Hence the computation of a pseudo-inverse matrix is involved. In this paper the numerical performance of different algorithms for Moore-Penrose pseudo-inverse computation have been tested for modal analysis of a four-flue chimney of a thermoelectrical plant. The computational scheme herein adopted for parameter identification is based on well-known modal properties and has a fast rate of convergence to solution. The computation of the Rayleigh damping coefficients a and fl is an important step in the area of the modal superposition technique. The proposed approach can accurately predict damping ratios and all the eigenvectors without evaluating mass and stiffness matrices. [ABSTRACT FROM AUTHOR]

In this paper we consider an inverse problem for a damped vibration system from the noisy measured eigendata, where the mass, damping, and stiffness matrices are all symmetric positive-definite matrices with the mass matrix being diagonal and the damping and stiffness matrices being tridiagonal. To take into consideration the noise in the data, the problem is formulated as a convex optimization problem involving quadratic constraints on the unknown mass, damping, and stiffness parameters. Then we propose a smoothing Newton-type algorithm for the optimization problem, which improves a pre-existing estimate of a solution to the inverse problem. We show that the proposed method converges both globally and quadratically. Numerical examples are also given to demonstrate the efficiency of our method. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The traditional neural system which conducts the paired association has the real coupling coefficients and is not suited to the implementation on digital processing LSI because of its analog property. From such a viewpoint, this paper applies the traditional idea of calculating the coupling coefficients on the real field to the binary field and proposes a system which conducts the paired association using only the logic operation. More precisely, it is noted that the associative law applies to the matrix operation on the real field as well as the matrix operation for the binary code. The coupling coefficients for the binary code for the paired association arc derived by applying the sweeping-out method to the matrix of binary numbers. By this approach, a paired-associate system is obtained by a simpler training algorithm with easy LSI implementation. This paper describes first the traditional solution of the paired-associate problem on the real field and then proposes a method of solution based on that approach for the paired-associate problem on the binary field. The existence condition for the solution of the paired- associate problem is discussed for the proposed method. Finally, the noise-reduction power of the proposed method is estimated. [ABSTRACT FROM AUTHOR]

Analysis of access sequences is an important technique in the mining of WWW access logs. The well-known apriori algorithm is a typical method. A problem of this method is that the obtained relation between sequences is not reflected in the output. This paper proposes a new method of sequence analysis using matrix clustering. This method considers a binary matrix in which the sequences correspond to the rows and ordered pairs of pages correspond to the columns. The similarities between sequences are extracted as clusters in the matrix. Based on these clusters, super-sequences, which are generalizations of similar sequences, can be generated. The proposed method is applied to real data and the results are evaluated. It is verified that the features of entire sequences can be extracted. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 90(10): 127–138, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20394 [ABSTRACT FROM AUTHOR]

This paper suggests a new type of mixture regression model, in which each mixture component is explained by its own regressors. Thus, the dependent variable can be driven by one of several unobservable explanatory mechanisms, each of which has its own distinct variables. An extension of the simulated annealing algorithm is introduced to fit this general mixture model. The paper also suggests a new technique for estimating the covariance matrix of estimators in a mixture model. Finally, empirical studies of a labour supply example show that our proposed model can perform much better than conventional logistic or mixture models. [ABSTRACT FROM AUTHOR]

This paper extends the weighted low rank approximation (WLRA) approach to linearly structured matrices. In the case of Hankel matrices with a special block structure, an equivalent unconstrained optimization problem is derived and an algorithm for solving it is proposed. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a method of moments (MoM) formulation for large thin-wire structures. In our approach, a modified version of the well-known Rao–Wilton–Glisson (RWG) basis functions for wires including a linear phase term is considered. This additional term allows an efficient representation of the travelling-wave modes on each wire, while it preserves the main advantages of RWG bases for arbitrarily complex wire topologies. The paper contains a detailed description of the algorithm used for the computation of the impedance matrix integrals. Finally, some results for scattering problems are presented to show the agreement with the conventional RWG-MoM solution. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 960–966, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21533 [ABSTRACT FROM AUTHOR]

The past 13 years have seen the development of many algorithms for approximating matrix functions in O(N) time, where N is the basis size. These O(N) algorithms rely on assumptions about the spatial locality of the matrix function; therefore their validity depends very much on the argument of the matrix function. In this article I carefully examine the validity of certain O(N) algorithms when applied to Hamiltonians of disordered systems. I focus on the prototypical disordered system, the Anderson model. I find that O(N) algorithms for the density matrix function can be used well below the Anderson transition (i.e. in the metallic phase;) they fail only when the coherence length becomes large. This paper also includes some experimental results about the Anderson model's behaviour across a range of disorders. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Many popular solution methods for large discrete ill-posed problems are based on Tikhonov regularization and compute a partial Lanczos bidiagonalization of the matrix. The computational effort required by these methods is not reduced significantly when the matrix of the discrete ill-posed problem, rather than being a general nonsymmetric matrix, is symmetric and possibly indefinite. This paper describes new methods, based on partial Lanczos tridiagonalization of the matrix, that exploit symmetry. Computed examples illustrate that one of these methods can require significantly less computational work than available structure-ignoring schemes. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]