Showing papers in "Linear Algebra and its Applications in 1991"

TL;DR: In this article, it was shown that the gradient flow on the space of orthogonal matrices can be used as an analog computer for solving genetic combinatorial optimization problems.

TL;DR: In this article, a primal-dual algorithm for linear programming is described, which allows for easy handling of simple bounds on the primal variables and incorporates free variables, which have not previously been included in a primal dual implementation.

TL;DR: In this article, the canonical forms under congruence for pairs of complex or real symmetric or skew matrices are established for skew matrix pairs, and the treatment is in the spirit of the well-known book of Gantmacher on matrix theory.

TL;DR: A method is given that does a better job of computing eigenvalues from the interior of the spectrum of a large matrix and a priori bounds can be given for the accuracy of interior eigenvalue and eigenvector approximations.

TL;DR: In this paper, a modified version of the Gauss-Seidel or Jacobi iterative method is proposed to solve a linear system Ax = b, where certain elementary row operations are performed on A before applying the GSE or JCI iterative methods and it is shown that when A is a nonsingular M -matrix or a singular tridiagonal M-matrix, the modified method yields considerable improvement in the rate of convergence.

TL;DR: In this article, an Arnoldi-based numerical method for solving a Sylvester-type equation arising in the construction of the Luenberger observer is proposed, where given an N × N matrix A and an n × m matrix G, the method simultaneously constructs an m × m Hessenberg matrix H with a pre-assigned spectrum and an X × m orthonormal matrix X such that AX − XH = G.

TL;DR: In this article, the distribution of the smallest eigenvalue of a matrix from the central Wishart distribution in the null case was given as a simple recursion, without resorting to zonal polynomials and hypergeometric functions of matrix arguments.

TL;DR: The theory of convergence of a generic GR algorithm for the matrix eigenvalue problem that includes the QR,LR,SR, and other algorithms as special cases is developed and it is shown that with a certain obvious shifting strategy the GR algorithm typically has a quadratic asymptotic convergence rate.

TL;DR: In this paper, two generalizations of the Kronecker product and two related generalisations of the vec operator are discussed. And the results of these generalizations pairwise match two different kinds of matrix partition, viz. the balanced and unbalanced ones.

TL;DR: In this paper, the Schur parameter pencil problem is solved in an O(n 3 )-time process using Householder eliminations, and it is backward stable in the sense that the condensed form is preserved throughout the process.

TL;DR: In this article, a new variable eigenvalue theory and an associated set of matrix canonical forms are developed for matrices over a differential ring, which include as special cases the classical companion, Jordan (diagonal), and (generalized) Vandermonde canonical forms.

TL;DR: In this paper, a new approach to the block SOR method applied to linear systems of equations which can be written as a matrix equation AX−XB=C was proposed.

TL;DR: This new algorithm is a generalization and improvement of the relaxed parallel multisplitting method, and based on the new algorithm model, is established another algorithm called the relaxation-based AOR algorithm, which convergence conditions are convenient to verify.

TL;DR: Different formulations of the operator c are given, its algebraic and geometric properties are discussed, and its operator norms are computed in different Banach algebras of matrices to give an efficient algorithm for finding the superoptimal circulant preconditioner.

TL;DR: It is shown how to generalize the ordinary singular value decomposition of a matrix into a combined factorization of any number of matrices, and proposed to call these factorizations generalized singularvalue decompositions.

TL;DR: In this article, a condition number for the linear complementarity problem (LCP) was defined, which characterizes the degree of difficulty for its solution when a potential reduction algorithm is used.

TL;DR: A graph-theoretic characterization of the generic structure at infinity of the transfer matrix of a structured system is developed and a structural version of two well-known disturbance decoupling problems is proposed.

TL;DR: In this paper, two partial orderings in the set of complex matrices are introduced by combining each of the conditions A*A = A*B and AA* = BA*, which define the star partial ordering.

TL;DR: In this paper, the authors characterize those △-matroids which can be obtained, as above, by means of a symmetric binary matrix, and characterize the set of △matroid pairs that satisfy the symmetric exchange axiom (SEA).

TL;DR: In this article, an approach to the computation of Lagrangian invariant subspaces of a Hamiltonian or a symplectic matrix was proposed, which is the missing link in the solution of the open problem of constructing a stable structure-preserving QR -like method of complexity O(n 3 ) for the computations of invariant subsets of Hamiltonian and symplectic matrices.

TL;DR: Three new iterative methods for the solution of the linear least squares problem with bound constraints are presented and their performance analyzed, with particular emphasis on the dependence on the starting point and the use of preconditioning for ill-conditioned problems.

TL;DR: This work considers the problem of minimizing a quadratic function with a knapsack constraint, and proposes and analyzes three algorithms based on simplicial partitioning and convex underestimating functions that can be used to compute the global optimum of indefinite Quadraticknapsack problems.

TL;DR: The algorithm, based on choice by value, compares favorably with the incomplete Choleski preconditioner and, equipped with a user-controlled parameter, is able to tackle extremely ill-conditioned problems arising in structural analysis, semiconductor simulation, oil-reservoir modelling, and other applications.

TL;DR: In this paper, an approach is proposed to generate a vertex solution while using a primal-dual interior point method to solve linear programs, where a controlled random perturbation is made to the cost vector.

TL;DR: A theorem is proved which gives a necessary and sufficient condition for ordering exact arithmetic CG processes for systems with different spectra according to the energy norm of the error.

TL;DR: In this article, a parametrization of the solution set of the algebraic Riccati equation and its inequality of optimal control is presented, where only sign-controllability of the underlying system is assumed.

TL;DR: In this paper, a triple diagonal matrix was studied extensively by Mark Kac in connection with problems in statistical mechanics, and it had been considered earlier by Sylvester and Schrodinger and later by Siegert and Hess.

TL;DR: In this article, some new comparison theorems for two nonnegative splittings (a splitting A = M − N is nonnegative if M −1 exists and M − 1 N is not negative) are derived.

TL;DR: A survey of canonical forms and invariants for unitary similarity can be found in this paper, where the authors give a detailed description of methods developed by several authors (Brenner, Littlewood, Mitchell, McRae, Radjavi, Sergeĭchuk, and Benedetti and Cragnolini).

TL;DR: In this paper, the disturbance localization problem and the problems of designing disturbance decoupled observers and of giving a geometric characterization of invariant zeros were solved for linear periodic discrete-time systems through an extension of the geometric approach, based on the notions of controlled invariant and conditionally invariant subspaces, to periodic ones.