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In the present paper we obtain an explicit closed-form solution for the discrete-time algebraic Riccati equation ( DTARE) with vanishing state weight, whenever the unstable eigenvalues are distinct. We discuss links to current algorithmic solutions and observe that the AREs in such a class solve on one hand the infimal signal-to-noise ratio ( SNR) problem, whilst on the other hand, in their dual form they solve a Kalman filter problem. We then extend the main result to an example case of the optimal linear quadratic regulator gain. We relax some of the assumptions behind the main result and conclude with possible future directions for the present work. [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]

In this paper, we consider the solution of linear systems of saddle point type by correcting the Uzawa algorithm, which has been proposed in [K. Arrow, L. Hurwicz, H. Uzawa, Studies in nonlinear programming, Stanford University Press, Stanford, CA, 1958]. We call this method as corrected Uzawa (CU) method. The convergence of the CU method is analyzed for solving nonsingular saddle point problem as well as the semi-convergence for the singular case. First, the corrected model for the Uzawa algorithm is established, and the CU algorithm is presented. Then we study the geometric meaning of the CU model. Moreover, we introduce the overall reduction coefficient α to measure the effect of the CU process. It is shown that the CU method converges faster than the Uzawa method and several other methods if the overall reduction coefficient α satisfies certain conditions. Numerical experiments are presented to illustrate the theoretical results and examine the numerical effectiveness of the CU method. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we present a primal-dual interior-point algorithm to solve a class of multi-objective network flow problems. More precisely, our algorithm is an extension of the single-objective primal infeasible dual feasible inexact interior point method for multi-objective linear network flow problems. Our algorithm is contrasted with standard interior point methods and experimental results on bi-objective instances are reported. The multi-objective instances are converted into single objective problems with the aid of an achievement function, which is particularly adequate for interactive decision-making methods. [ABSTRACT FROM AUTHOR]

This paper develops a general framework for applying algebraic multigrid techniques to constrained systems of linear algebraic equations that arise in applications with discretized PDEs. We discuss constraint coarsening strategies for constructing multigrid coarse grid spaces and several classes of multigrid smoothers for these systems. The potential of these methods is investigated with their application to contact problems in solid mechanics. Published in 2004 by John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

To solve the problem of state estimation for systems with dual noise terms, a zonotope and Gaussian Kalman filters based state estimation algorithm is proposed. A state estimator is designed to obtain the estimation interval of the true state in the presence of both stochastic and unknown but bounded (UBB) uncertainties. A novel coefficient that weighs the relative influence of stochastic and UBB uncertainties is introduced, and the optimal weight solution is introduced by minimizing the polyhedron space and mean square error. Finally, two simulation examples are presented to demonstrate the accuracy and effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

SUMMARY We give two generalizations of the induced dimension reduction (IDR) approach for the solution of linear systems. We derive a flexible and a multi-shift quasi-minimal residual IDR variant. These variants are based on a generalized Hessenberg decomposition. We present a new, more stable way to compute basis vectors in IDR. Numerical examples are presented to show the effectiveness of these new IDR variants and the new basis compared with existing ones and to other Krylov subspace methods. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY We consider the pole assignment problems for time-invariant linear and quadratic control systems, with time-delay in the control. Closed-loop eigenvectors in X = [ x1, x2, ⋯ ] are chosen from their corresponding invariant subspaces, possibly optimizing some robustness measure, and explicit expressions for the feedback matrices are given in terms of X. Condition of the problems is also investigated. Our approach extends the well-known Kautsky, Nichols, and Van Dooren algorithm. Consequently, the results are similar to those for systems without time-delay, except for the presence of the 'secondary' eigenvalues and the condition of the problems. Simple illustrative numerical examples are given. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY We propose a generalization of the structured doubling algorithm to compute invariant subspaces of structured matrix pencils that arise in the context of solving linear quadratic optimal control problems. The new algorithm is designed to attain better accuracy when the classical Riccati equation approach for the solution of the optimal control problem is not well suited because the stable and unstable invariant subspaces are not well separated (because of eigenvalues near or on the imaginary axis) or in the case when the Riccati solution does not exist at all. We analyze the convergence of the method and compare the new method with the classical structured doubling algorithm as well as some structured QR methods. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This article reports on experiences with aggregation algebraic multigrid relying on Krylov acceleration on each level of the grid hierarchy as preconditioners for linear systems in general purpose fluid flow simulation software. In benchmarks that reflect the requirements of industrial simulations, it is demonstrated that for semi-definite problems, the performance of recently published algorithms of this type is very attractive but that proposed variants of these algorithms occasionally fail for nonsymmetric problems. A modification leading to reliable solvers is suggested. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

To iterative solve large dense complex linear systems arising from electric field integral equations formulation of electromagnetic scattering problems, multilevel fast multipole algorithm (MLFMA) is built to speed up the matrix-vector product (MVP) operations. This article presents a novel flexible generalized minimum residual with deflated restarted (FGMRES-DR), which can greatly improve the convergence of those large dense complex linear systems. Based on physical mechanism of the scattering problems, in inner iteration of FGMRES-DR, an iterative solution of the near-field matrix in MLFMA is adopted. In outer iteration, deflation method which is purely algebraic is used to eliminate the influence on convergence because of the smallest eigenvalues. Numerical experiments indicate that FGMRES-DR is very effective and can reduce the number of MVP compared with the FGMRES in large-scale electromagnetic problems. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:1360-1364, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26019 [ABSTRACT FROM AUTHOR]