Search

The stabilization problem of state observer based for linear discrete-time periodic (LDP) system and its robust consideration are discussed in this paper. It is proved that the periodic controller and the full-dimensional periodic state observer can be designed separately. Based on the well-known CGalgorithm for matrix equation Ax = b as well as applying the lifting technique and algebraic operations, an iterative algorithm for both periodic observer gains and periodic state feedback gains can be generated simultaneously. By optimizing the free parameter matrix in the proposed algorithm, a robust stabilization algorithm based on periodic observer for LDP systems is presented. One numerical example is worked out to illustrate the effect of the proposed approaches. [ABSTRACT FROM AUTHOR]

Conjugate gradient methods are widely used for solving unconstrained optimization and nonlinear equations, specially in large-scale cases. Since they own the attractive practical factors of simple computation and low memory requirement, interesting theoretical features of curvature information and strong global convergence. In this paper, we present a modified conjugate gradient algorithm by line search method with acceleration scheme for nonlinear symmetric equations. Furthermore, the proposed method not only possess descent property but also owns global convergence in mild conditions. Numerical results also indicate that the presented method is much more effective than the other methods for the test problems. [ABSTRACT FROM PUBLISHER]

Purpose – The linear matrix equations have wide applications in engineering, physics, economics and statistics. The purpose of this paper is to introduce iterative methods for solving the systems of linear matrix equations. Design/methodology/approach – According to the hierarchical identification principle, the authors construct alternating direction gradient-based iterative (ADGI) methods to solve systems of linear matrix equations. Findings – The authors propose efficient ADGI methods to solve the systems of linear matrix equations. It is proven that the ADGI methods consistently converge to the solution for any initial matrix. Moreover, the constructed methods are extended for finding the reflexive solution to the systems of linear matrix equations. Originality/value – This paper proposes efficient iterative methods without computing any matrix inverses, vec operator and Kronecker product for finding the solution of the systems of linear matrix equations. [ABSTRACT FROM AUTHOR]

This paper proposes a kinematics model with four noncoplanar points’ Cartesian coordinates for a spatial parallel manipulator, which is called the tetrahedron coordinate method. The sufficient and necessary criteria of utilizing the Cartesian coordinates of the four noncoplanar points are proved. Because the constraint equations are either quadratic or linear, and the coordinates are complete Cartesian, the derivative matrix of the constraint equations only consists of linear or constant elements that are the advantages of the general natural coordinate method as well. However, the number of variables of the general natural coordinate method will increase with the increasing number of investigated points. The tetrahedron coordinate approach proposed in this paper does not need to induce any new variables when more points on the manipulator are considered. As a result, it has a prevailing advantage over the general natural coordinate method. This advantage is especially explicit when establishing the kinematics models for complex spatial parallel manipulators with three to six degrees of freedom, the virtues of which are demonstrated by a case study. [ABSTRACT FROM PUBLISHER]

Purpose |!|#8211; The purpose of this paper is to find two iterative methods to solve the general coupled matrix equations over the generalized centro-symmetric and central antisymmetric matrices. Design/methodology/approach |!|#8211; By extending the idea of conjugate gradient (CG) method, the authors present two iterative methods to solve the general coupled matrix equations over the generalized centro-symmetric and central antisymmetric matrices. Findings |!|#8211; When the general coupled matrix equations are consistent over the generalized centro-symmetric and central anti-symmetric matrices, the generalized centro-symmetric and central anti-symmetric solutions can be obtained within nite iterative steps. Also the least Frobenius norm generalized centrosymmetric and central anti-symmetric solutions can be derived by choosing a special kind of initial matrices. Furthermore, the optimal approximation generalized centrosymmetric and central anti-symmetric solutions to given generalized centro-symmetric and central anti-symmetric matrices can be obtained by finding the least Frobenius norm generalized centro-symmetric and central anti-symmetric solutions of new matrix equations. The authors employ some numerical examples to support the theoretical results of this paper. Finally, the application of the presented methods is highlighted for solving the projected generalized continuous-time algebraic Lyapunov equations (GCALE). Originality/value |!|#8211; By the algorithms, the solvability of the general coupled matrix equations over generalized centro-symmetric and central anti-symmetric matrices can be determined automatically. The convergence results of the iterative algorithms are also proposed. Several examples and an application are given to show the efficiency of the presented methods. [ABSTRACT FROM AUTHOR]

This paper describes a design for a least mean square error estimator in discrete time systems where the components of the state vector, in measurement equation, are corrupted by different multiplicative noises in addition to observation noise. We show how known results can be considered a particular case of the algorithm stated in this paper. [ABSTRACT FROM AUTHOR]

Abstract: A Cramer rule for solving a kind of restricted matrix equationsis presented in [G. Wang, Jie Sun, A Cramer rule for solution of the general restricted matrix equation, Appl. Math. Comput. 154 (2004) 415–422]. This paper gives a more condensed Cramer rule for the solution of the matrix equations. The results in [G. Wang, Z.L. Xu, Solving a kind of restricted matrix equations and Cramer rule, Appl. Math. Comput. 162 (2005) 329–338, Chao Gu, G.R. Wang, Z.L. Xu, PCR Algorithm for the Parallel Computation of the Solution of a class of Singular linear Systems, Appl. Math. Comput. 176 (2006) 237–244] are partially the special cases in our paper. [Copyright &y& Elsevier]

Abstract: The present paper describes an efficient algorithm to integrate the equations of motion implicitly in the frequency domain. The standard FEM displacement model (Galerkin formulation) is employed to perform space discretization, and the time-marching process is carried out through an algorithm based on the Green’s function of the mechanical system in nodal coordinates. In the present formulation, mechanical system Green’s functions are implicitly calculated in the frequency domain. Once the Green’s functions related matrices are computed, a time integration procedure, which demands low computational effort when applied to non-linear mechanical systems, becomes available. At the end of the paper numerical examples are presented in order to illustrate the accuracy of the present approach. [Copyright &y& Elsevier]

A new algorithm for ranking the input features and obtaining the best feature subset is developed and illustrated in this paper. The asymptotic formula for mutual information and the expectation maximisation (EM) algorithm are used to developing the feature selection algorithm in this paper. We not only consider the dependence between the features and the class, but also measure the dependence among the features. Even for noisy data, this algorithm still works well. An empirical study is carried out in order to compare the proposed algorithm with the current existing algorithms. The proposed algorithm is illustrated by application to a variety of problems. [ABSTRACT FROM AUTHOR]

In this paper, we consider the convergence criteria for iterative algorithms of Uzawa type for solving linear saddle point problems. Theoretically weaker convergence criteria than before are established for the general case and these are used to deduce conditions for convergence of two special cases: the exact Uzawa algorithm and the linear one-step method. The conclusions given here hold for both symmetric and nonsymmetric saddle point problems. These new sufficient conditions are compared with some known results and illustrated by two examples. Numerical experiments to verify the conclusions in this paper for the preconditioned exact Uzawa algorithm are provided. [Copyright &y& Elsevier]

This paper studies the limiting behavior of weighted infeasible central paths for semidefinite programming (SDP) obtained from centrality equations of the form X½ SX½ = vW, where W is a fixed positive definite matrix and v>0 is a parameter, under the assumption that the problem has a strictly complementary primal-dual optimal solution. It is shown that a weighted central path as a function of √v can be extended analytically beyond 0 and hence that the path converges as v↓0. Characterization of the limit points of the path and its normalized first-order derivatives are also provided. As a consequence, it is shown that a weighted central path can have two types of behavior: it converges either as &Tetha;(v) or asT &Tetha;(√v) depending on whether the matrix W on a certain scaled space is block diagonal or not, respectively. We also derive an error bound on the distance between a point lying in a certain neighborhood of the central path and the set of primal-dual optimal solutions. Finally, in light of the results of this paper, we give a characterization of a sufficient condition proposed by Potra and Sheng which guarantees the superlinear convergence of a class of primal-dual interior-point SDP algorithms. [ABSTRACT FROM AUTHOR]

In two previous papers, the two first-named authors introduced a notion of contact r-surgery along Legendrian knots in contact 3-manifolds. They also showed how (at least in principle) to convert any contact r-surgery into a sequence of contact (± 1)-surgeries, and used this to prove that any (closed) contact 3-manifold can be obtained from the standard contact structure on S3 by a sequence of such contact (± 1)-surgeries. In the present paper, we give a shorter proof of that result and a more explicit algorithm for turning a contact r-surgery into (± 1)-surgeries. We use this to give explicit surgery diagrams for all contact structures on S3 and S1 x S2, as well as all overtwisted contact structures on arbitrary closed, orientable 3-manifolds. This amounts to a new proof of the Lutz-Martinet theorem that each homotopy class of 2-plane fields on such a manifold is represented by a contact structure. [ABSTRACT FROM AUTHOR]

The development of a novel second-order accurate both in time and space kinetic scheme, called the Kinetic Wave/Particle Split (KWPS) scheme is reported in this paper. It is demonstrated that the first-order KWPS algorithm, while computationally efficient and robust, is very diffusive on a reasonable mesh. The KWPS scheme is derived by employing the following steps: the molecular velocity in the Boltzmann equation is split as a sum of fluid velocity and thermal (peculiar) velocity, thus the flux vector in the Boltzmann equation is divided into a convective part and an acoustic part. The Boltzmann equation is then discretized using an upwind differencing. Moments of the discretized Boltzmann equation with the collision invariant vector and Maxwellian distribution function then yield the KWPS scheme for the Euler equations. The second-order formulation is obtained through the application of a Taylor series expansion of the Maxwellian distribution function to include the first-order derivatives. Numerical test cases, both in 1-D and 2-D, are computed to demonstrate the improved accuracy of the second-order KWPS scheme, while maintaining both the efficiency and robustness of the first-order scheme. It should be noted that the new second-order KWPS formulation cannot be obtained using the standard numerical approach employed in the literature for second-order extension. The methodology employed in this paper can be easily extended to formulate a KWPS scheme to any order of accuracy. [Copyright &y& Elsevier]

In this paper, the traffic performance of dynamic channel assignment (DCA) in cellular mobile system with hand-off is investigated. A traffic model for cellular system incorporating hand-off is established first. Under the framework of the model, a hand-off priority scheme is developed to reduce the forced termination of calls in progress. This paper analyses and derives the traffic performance bound for DCA strategies with hand-off by extending the maximum packing (MP) scheme to include the hand-off procedure. For practical implementation, a distributed DCA algorithm (DDCA) is also proposed. A non-priority scheme and the proposed priority scheme can be combined with either MP or DDCA. It is shown that the simulation results of DDCA scheme are comparable with the analytical bounds given by MP for both the non-prioritized case and prioritized case. A reasonable trade-off between the new call blocking probability and forced termination probability can be achieved by using the proposed prioritized scheme in DCA. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper introduces stochastic weighted particle algorithms for the solution of multi-compartment population balance equations. In particular, it presents a class of fragmentation weight transfer functions which are constructed such that the number of computational particles stays constant during fragmentation events. The weight transfer functions are constructed based on systems of weighted computational particles and each of it leads to a stochastic particle algorithm for the numerical treatment of population balance equations. Besides fragmentation, the algorithms also consider physical processes such as coagulation and the exchange of mass with the surroundings. The numerical properties of the algorithms are compared to the direct simulation algorithm and an existing method for the fragmentation of weighted particles. It is found that the new algorithms show better numerical performance over the two existing methods especially for systems with significant amount of large particles and high fragmentation rates. [ABSTRACT FROM AUTHOR]

This paper proposes an iterative approximation technique of log-magnitude response for IIR filters. Minimization of the mean-square error between a desired log-frequency response and that of an IIR filter leads to a nonlinear problem. In this paper, the least squares problem on the logarithmic scale is approximated by the iteration of a weighted least squares problem on the linear scale. The weighting function is updated using the result of the previous iteration so that the weighted error on the linear scale approximates the squared error on the logarithmic scale. The filter coefficients at each iteration step can efficiently be obtained using a fast recursive algorithm for a set of linear equations. Several design examples are presented, which show that the iterative algorithm converges after one or two iterations in practice and the weighted error at convergence gives a good, estimate of the mean-square error on the logarithmic scale. An example is also presented, where both log-magnitude and phase responses are approximated simultaneously. [ABSTRACT FROM AUTHOR]

To provide generalized solutions if a given problem admits no actual solution is an important task in mathematics and the natural sciences. It has a rich history dating back to the early 19th century, when Carl Friedrich Gauss developed the method of least squares of a system of linear equations--its solutions can be viewed as fixed points of averaged projections onto hyperplanes. A powerful generalization of this problem is to find fixed points of averaged resolvents (i.e., firmly nonexpansive mappings). This paper concerns the relationship between the set of fixed points of averaged resolvents and certain fixed point sets of compositions of resolvents. It partially extends recent work for two mappings on a question of C. Byrne. The analysis suggests a reformulation in a product space. Algorithmic consequences are also presented. [ABSTRACT FROM AUTHOR]

When using interior methods for solving semidefinite programming (SDP), one needs to solve a system of linear equations at each iteration. For problems of large size, solving the system of linear equations can be very expensive. In this paper, based on a semismooth equation reformulation using Fischer's function, we propose a filter method with trust region for solving large-scale SDP problems. At each iteration we perform a number of conjugate gradient iterations, but do not need to solve a system of linear equations. Under mild assumptions, the convergence of this algorithm is established. Numerical examples are given to illustrate the convergence results obtained. [ABSTRACT FROM AUTHOR]

Abstract: According to the hierarchical identification principle, a hierarchical gradient based iterative estimation algorithm is derived for multivariable output error moving average systems (i.e., multivariable OEMA-like models) which is different from multivariable CARMA-like models. As there exist unmeasurable noise-free outputs and unknown noise terms in the information vector/matrix of the corresponding identification model, this paper is, by means of the auxiliary model identification idea, to replace the unmeasurable variables in the information vector/matrix with the estimated residuals and the outputs of the auxiliary model. A numerical example is provided. [ABSTRACT FROM AUTHOR]

Model-based analysis and synthesis applied to the dynamics, guidance, and control of an autonomous undersea vehicle are presented. As the dynamic model for describing vehicle motion mathematically, the equations of motion are derived. The stability derivatives in the equations of motion are determined by a simulation-based technique using computational fluid dynamics analysis. The dynamic model is applied to the design of the low-level control systems, offering model-based synthetic approach in dynamics and control applications. As an intelligent navigational strategy for undersea vehicles, we present the optimal guidance in environmental disturbances. The optimal guidance aims at the minimum-time transit of a vehicle in an environmental flow disturbance. In this paper, a newly developed algorithm for obtaining the numerical solution of the optimal guidance law is presented. The algorithm is a globally working procedure deriving the optimal guidance in any deterministic environmental disturbance. As a fail-safe tactic in achieving the optimal navigation in environments of moderate uncertainty, we propose the quasi-optimal guidance. Performances of the optimal and the quasi-optimal guidances are demonstrated by the simulated navigations in a few environmental disturbances. [ABSTRACT FROM AUTHOR]

The aim of this paper is to describe a quadratic algorithm for computing the equation K-automaton of a regular K-expression as defined by Lombardy and Sakarovitch. Our construction is based on an extension to regular K-expressions of the notion of c-continuation that we introduced to compute the equation automaton of a regular expression as a quotient of its position automaton. [ABSTRACT FROM AUTHOR]

The paper suggests constraints on the coefficients ai, bi, ci j of the bilinear continuous-time input-output model that yield generalized state equations with input derivative order lower than that in the input-output equations. In the limiting case when one removes the input derivatives altogether, these conditions provide a solution of the realizability problem. The new state coordinates are found step by step. We first find a coordinate transformation allowing the reduction of the maximal order of the input time derivatives by one and write the corresponding state equations. At the second step we find the next coordinate transformation to lower the maximal order of input time derivative in the new state equations, etc. At each step we check, what condition the coefficients should satisfy to make the next step possible. [ABSTRACT FROM AUTHOR]

The goal of this paper is to prove the first and second order optimality conditions for some control problems governed by semilinear elliptic equations with pointwise control constraints and finitely many equality and inequality pointwise state constraints. To carry out the analysis we formulate a regularity assumption which is equivalent to the first order optimality conditions. Though the presence of pointwise state constraints leads to a discontinuous adjoint state, we prove that the optimal control is Lipschitz in the whole domain. Necessary and sufficient second order conditions are proved with a minimal gap between them. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we investigate the convergence of subdivision schemes associated with masks being polynomially decay sequences. Two-scale vector refinement equations are the formwhere the vector of functions is in and is polynomially decay sequence of matrices called refinement mask. Associated with the mask a is a linear operator on given byBy using same methods in [B. Han, R. Q. Jia, Characterization of Riesz bases of wavelets generated from multiresolution analysis, manuscript]; [B. Han, Refinable functions and cascade algorithms in weighted spaces with infinitely supported masks, manuscript]; [R.Q. Jia, Q.T. Jiang, Z.W. Shen, Convergence of cascade algorithms associated with nonhomogeneous refinement equations, Proc. Amer. Math. Soc. 129 (2001) 415–427]; [R.Q. Jia, Convergence of vector subdivision schemes and construction of biorthogonal multiple wavelets, in: Advances in Wavelet, Hong Kong,1997, Springer, Singapore, 1998, pp. 199–227], a characterization of convergence of the sequences in the -norm is given, which extends the main results in [R.Q. Jia, S.D. Riemenschneider, D.X. Zhou, Vector subdivision schemes and multiple wavelets, Math. Comp. 67 (1998) 1533–1563] on convergence of the subdivision schemes associated with a finitely supported mask to the case in which mask a is polynomially decay sequence. As an application, we also obtain a characterization of smoothness of solutions of the refinement equation mentioned above for the case . [Copyright &y& Elsevier]

Based on the generalized minimal residual (GMRES) principle, Hu and Reichel proposed a minimal residual algorithm for the Sylvester equation. The algorithm requires the solution of a structured least squares problem. They form the normal equations of the least squares problem and then solve it by a direct solver, so it is susceptible to instability. In this paper, by exploiting the special structure of the least squares problem and working on the problem directly, a numerically stable QR decomposition based algorithm is presented for the problem. The new algorithm is more stable than the normal equations algorithm of Hu and Reichel. Numerical experiments are reported to confirm the superior stability of the new algorithm. [ABSTRACT FROM AUTHOR]

The filter generator is an important building block in many stream ciphers. The generator consists of a linear feedback shift register of length n that generates an m-sequence of period 2′ - 1 filtered through a Boolean function of degree d that combines bits from the shift register and creates an output bit zt at any time t. The previous best attacks aimed at reconstructing the initial state from an observed keystream, have essentially reduced the problem to solving a nonlinear system of D = (Multiple line equation(s) cannot be represented in ASCII text) (i) equations in n unknowns using techniques based on linear algebra. This attack needs about D bits of keystream and the system can be solved in complexity O (Dω), where ω can be taken to be Strassen's reduction exponent ω = log2 (7) ≈ 2.807. This paper describes a new algorithm that recovers the initial state of most filter generators after observing O(D) keystream bits with complexity O((D - n)/2) ≈ O(D), after a pre-computation with complexity O(D(log2 D)³). [ABSTRACT FROM AUTHOR]

Abstract: Exclusion algorithms have been used recently to find all solutions of a system of nonlinear equations or to find the global minimum of a function over a compact domain. These algorithms are based on a minimization condition that can be applied to each cell in the domain. In this paper, we consider Lipschitz functions of order and give a new minimization condition for the exclusion algorithm. Furthermore, convergence and complexity results are presented for such algorithm. [Copyright &y& Elsevier]

Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically by introducing anartificial timevariable. The actual computational model involves a discretization of the now time-dependent differential system, usually employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be ?close enough? to the dynamics of the continuous system (which is typically easier to analyze) provided that small ? hence many ? time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process can be improved to better reflect the actual properties sought. In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling approach may possibly lead to algorithms with improved efficiency. [ABSTRACT FROM AUTHOR]

The Peaceman-Rachford and Douglas-Rachford operator splitting methods are advantageous for solving variational inequality problems, since they attack the original problems via solving a sequence of systems of smooth equations, which are much easier to solve than the variational inequalities. However, solving the subproblems exactly may be prohibitively difficult or even impossible. In this paper, we propose an inexact operator splitting method, where the subproblems are solved approximately with some relative error tolerance. Another contribution is that we adjust the scalar parameter automatically at each iteration and the adjustment parameter can be a positive constant, which makes the methods more practical and efficient. We prove the convergence of the method and present some preliminary computational results, showing that the proposed method is promising. [ABSTRACT FROM AUTHOR]

Abstract: Solving nonlinear equations is a problem often needed to be dealt with in the practical engineering application. This paper discusses preconditioning methods based on Block Broyden method. It first introduces the Block Broyden method and preconditioning technique. Then it presents four different preconditioners for the Block Broyden method and discusses the implementation process. It also analyzes the time complexity of the four algorithms. Finally, it solves the nonlinear systems arising from the Bratu problem by the four preconditioning algorithms. Experimental results show that the preconditioning technique is effective for the Block Broyden method and that the preconditioner SSOR has the fastest solving speed and the best performance among the four preconditioners. Therefore, it can be used in the large-scale problems arising from scientific and engineering computing. [Copyright &y& Elsevier]

This paper considers a class of iterative message- passing decoders for low-density parity-check codes in which the decoder can choose its decoding rule from a set of decoding algorithms at each iteration. Each available decoding algorithm may have a different per-iteration computation time and performance. With an appropriate choice of algorithm at each iteration, overall decoding latency can be reduced significantly, compared with standard decoding methods. Such a decoder is called a gear-shift decoder because it changes its decoding rule (shifts gears) in order to guarantee both convergence and maximum decoding speed (minimum decoding latency). Using extrinsic information transfer charts, the problem of finding the optimum (minimum decoding latency) gear-shift decoder is formulated as a computationally tractable dynamic program. The optimum gear-shift decoder is proved to have a decoding threshold equal to or better than the best decoding threshold among those of the available algorithms. In addition to speeding up software decoder implementations, gear-shift decoding can be applied to optimize a pipelined hardware decoder, minimizing hardware cost for a given decoder throughput. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to state a random version of the completely generalized nonlinear variational inclusions for a nonempty compact and convex subset of a Hilbert space and to show its equivalence with a class of random proximal operator equations. Using the equivalence, the random iterative algorithms for the class of inclusions has been developed and it has been proved that the approximate random solutions obtained by this random algorithms converges to the exact random solutions of this class of random variational inclusions. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the prediction of the overall behavior of a class of two-phase elasto-viscoplastic composites, based on mean-field homogenization. For this, important improvements are made to the recently-proposed affine formulation. The latter theory linearizes the rate-dependent inelastic constitutive equations of each phase’s material and transforms them into fictitious linear thermo-elastic relations in the Laplace–Carson domain. The main contributions of the present work are threefold. Firstly, complete mathematical developments including a full treatment of internal variables are carried out, enabling the modeling of the response under unloading and cyclic histories. Secondly, robust and accurate computational algorithms are proposed. Thirdly, an extensive validation of the predictions against reference unit cell finite element results is conducted for a variety of materials and loadings. A good agreement between predictions and reference results is observed. [Copyright &y& Elsevier]

In this paper, we introduce the doubling transformation, a structure-preserving transformation for symplectic pencils, and present its basic properties. Based on these properties, a unified convergence theory for the structure-preserving doubling algorithms for a class of Riccati-type matrix equations is established, using only elementary matrix theory. [ABSTRACT FROM AUTHOR]

In this paper, by using a so-called fixed steplength strategy, we propose a BFGS method without use of line searches for unconstrained optimization. Under mild conditions, we show the global and superlinear convergence of the proposed method even when the objective function is nonconvex. [ABSTRACT FROM AUTHOR]

The solution of large sparse linear systems of equations is one of the cornerstones of scientific computation. In many applications it is important to be able to solve these systems as rapidly as possible. One approach for very large problems is to reorder the system matrix to bordered block diagonal form and then to solve the block system using a coarse-grained parallel approach. In this paper, we consider the problem of efficiently ordering unsymmetric systems to singly bordered block diagonal form. Algorithms such as the MONET algorithm of Hu et al. (Comput. Chem. Eng. 23 (2000) 1631) that depend upon computing a representation of AAT can be prohibitively expensive when a single (or small number of) matrix factorizations are required. We therefore work with the graph of AT + A (or BT + B, where B is a row permutation of A) and propose new reordering algorithms that use only vertex separators and wide separators of this graph. Numerical experiments demonstrate that our methods are efficient and can produce bordered forms that are competitive with those obtained using MONET. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we describe in detail the computational algorithm used by our parallel multigrid elliptic equation solver with adaptive mesh refinement. Our code uses truncation error estimates to adaptively refine the grid as part of the solution process. The presentation includes a discussion of the orders of accuracy that we use for prolongation and restriction operators to ensure second order accurate results and to minimize computational work. Code tests are presented that confirm the overall second order accuracy and demonstrate the savings in computational resources provided by adaptive mesh refinement. [Copyright &y& Elsevier]

Abstract: In this paper, we present some efficient numerical algorithms for solving a system of two nonlinear equations (with two variables) based on Newton’s method. The modified Adomian decomposition method is applied to construct the numerical algorithms. Some numerical illustrations are given to show the efficiency of algorithms. [Copyright &y& Elsevier]

In this paper it is shown that the Doubling Algorithm for solving the discrete time Riccati Equation also provides the steady state solution of a related dual Riccati Equation. [ABSTRACT FROM AUTHOR]

The estimation of a circle's centre and radius from a set of noisy measurement of its circumference has many applications. It is problem of fitting a circle to the measurement and the fit can be in algebraic or geometric distance. The former gives linear equations, while the latter yields nonlinear equations. Starting from estimation theory, this paper first proves that the maximum likelihood (ML), i.e., the optimal estimation of the circle parameters, is equivalent to the minimization of the geometric distances. It then derives a pseudolinear set of ML equations whose coefficients are functions of the unknowns. An approximate ML algorithm updates the coefficients from the previous solution and selects the solution that gives the minimum cost. Simulation results show that the ML algorithm attains the Cramer-Rao lower bound (CRLB) for arc sizes as small as 90℃. For arc sizes of 15℃ and 5℃ the Ml algorithm errors are slightly above the CRLB, but lower than those of other linear estimators. [ABSTRACT FROM AUTHOR]

We consider the problem of finding solutions of systems of monotone equations. The Newton-type algorithm proposed in Ref. 1 has a very nice global convergence property in that the whole sequence of iterates generated by this algorithm converges to a solution, if it exists. Superlinear convergence of this algorithm is obtained under a standard nonsingularity assumption. The nonsingularity condition implies that the problem has a unique solution; thus, for a problem with more than one solution, such a nonsingularity condition cannot hold. In this paper, we show that the superlinear convergence of this algorithm still holds under a local error-bound assumption that is weaker than the standard nonsingularity condition. The local error-bound condition may hold even for problems with nonunique solutions. As an application, we obtain a Newton algorithm with very nice global and superlinear convergence for the minimum norm solution of linear programs. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a second-order scheme of precision integration for dynamic analysis with respect to long-term integration. Rather than transforming into first-order equations, a recursive scheme is presented in detail for direct solution of the homogeneous part of second-order algebraic and differential equations. The sine and cosine matrices involved in the scheme are calculated using the so-called 2 N algorithm. Numerical tests show that both the efficiency and the accuracy of homogeneous equations can be improved considerably with the second-order scheme. The corresponding particular solution is also presented, incorporated with the second-order scheme where the excitation vector is approximated by the truncated Taylor series. [Copyright &y& Elsevier]

Abstract: The goal of this paper is to describe an efficient cost-effective mathematical modelfor controlling the Czochralski crystal growth process. We first consider the governing equations for a class of MHD problems. We then choose the use of an externally applied magnetic field as a control mechanism. We examine theoretical and numerical results applicable to the optimal control of evolutionary magnetically conducted flows. The appropriate state equations are derived. First-order necessary conditions are examined. Next, we develop numerical methods for solving the necessary conditions of optimality, and alternative cost-efficient algorithms are discussed. Finally, these results are used to design a control strategy for the Czochralski crystal growth process. [Copyright &y& Elsevier]

The present paper describes the development and the performance of parallel FEM software for solving various CFD problems. Domain decomposition strategy and parallel iterative GMRES solver have been adapted to the universal space‐time FEM code FEMTOOL, which allows implementation of any partial differential equation with minor expenses. The developed data structures, the static load balancing and the inter‐processor communication algorithms have been particularly suited for homogeneous distributed memory PC clusters. The universality of the considered parallel algorithms has been validated solving applications described by the Poisson equation, by the convective transport equation and by the Navier–Stokes equations. Three typical benchmark problems have been solved in order to perform the efficiency study. The performance of parallel computations, the speed‐up and the efficiency have been measured on three BEOWULF PC clusters as well as on the cluster of IBM RISC workstations and on the IBM SP2 supercomputer. [ABSTRACT FROM AUTHOR]

In this paper we develop techniques for computing elementwise conservative approximations of the flux on element boundaries for the continuous Galerkin method. The technique is based on computing a correction of the average normal flux on an edge or face. The correction is a jump in a piecewise constant or linear function. We derive a basic algorithm which is based on solving a global system of equations and a parallel algorithm based on solving local problems on stars. The methods work on meshes with different element types and hanging nodes. We prove existence, uniqueness, and optimal order error estimates. Lastly, we illustrate our results by a few numerical examples. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, some new oscillation criteria are obtained for the first-order delay difference equation , where k,l1,l2,, ls are positive integer numbers, f is a function. Our results improve the known results in the literature. And some examples are given to demonstrate the advantage of our results. [Copyright &y& Elsevier]

Abstract: In this paper, we establish some oscillation criteria for the neutral difference equation with positive and negative coefficients without the limitation of condition cn + Σn−1i=n−π + α qi ≤ 1, where cn, pn, and qn are nonnegative integers with τ − 1 ≥ maxσ,γ, γ ≥ 1, σ ≥ 0. [Copyright &y& Elsevier]

In Ref. [J. Comput. Math. 20 (3) (2002) 301], a new superlinearly convergent algorithm of sequential systems of linear equations for nonlinear optimization problems with inequality constraints was proposed. Since the new algorithm only needs to solve four systems of linear equations having a same coefficient matrix per iteration, the computation amount of the algorithm is much less than that of the existing sequential quadratic programming algorithms per iteration. Under some mild assumptions, the new algorithm is globally convergent and its rate of convergence is one-step superlinearly. In this paper, it is shown that the new algorithm also can be used to deal with nonlinear optimization problems having nonlinearly equality and inequality constraints, by solving an auxiliary problem. Some numerical results are reported. [Copyright &y& Elsevier]

The paper deals with the three-dimensional dynamic problem for an elliptic crack interacting with a normally incident harmonic compression–expansion wave, considering the contact interaction of the crack faces. An asymmetric solution is obtained using an iteration algorithm developed earlier. Numerical results are presented [ABSTRACT FROM AUTHOR]

Many characterizations of semipreconnected (=β-connected) spaces are obtained by Aho and Nieminen [2]. In this paper, we obtain further characterizations of semipreconnected spaces. We introduce β-separated and βs-connected sets and by using these sets we obtain several properties of β-connected subspaces. [ABSTRACT FROM AUTHOR]