Topic
Square matrix
About: Square matrix is a research topic. Over the lifetime, 5000 publications have been published within this topic receiving 92428 citations.
Papers published on a yearly basis
Papers
More filters
••
TL;DR: In this article, the variation of the Jordan structure of a complex square matrix when small perturbations on the elements of one row is studied, and it is shown that the variation depends on the size of the perturbation.
22 citations
••
TL;DR: An algorithm which could be considered an improvement to the well-known Schulz iteration for finding the inverse of a square matrix iteratively is presented and its computational complexity is analysed.
Abstract: In this paper, we present an algorithm which could be considered an improvement to the well-known Schulz iteration for finding the inverse of a square matrix iteratively. The convergence of the proposed method is proved and its computational complexity is analysed. The extension of the scheme to generalized outer inverses will be treated. In order to validate the new scheme, we apply it to large sparse matrices alongside the application to preconditioning of practical problems.
22 citations
••
TL;DR: An algorithm to compute the singular value decomposition (SVD) of time-varying square matrices is concerned with, whose solutions asymptotically track the diagonalizing transformation.
22 citations
••
01 Jan 1980
TL;DR: In this article, a review on the matrix generalization of the inverse scattering method is presented, where the authors show that the same generalization is possible for discrete cases (lattice problems).
Abstract: This is a review on the matrix generalization of the inverse scattering method. First, the inverse scattering problem for n × n Schrodinger equation is discussed. Second, the inverse scattering method is extended into n × n matrix form. Nonlinear evolution equations which are solvable by the extension are presented. In addition, it is pointed out that the same generalization is possible for discrete cases (lattice problems).
22 citations
17 Dec 1971
TL;DR: The authors present some new mathematical results for matrix polynomials, as well as a globally convergent algorithm for calculating such solvents, and algorithms are presented which generalize Traub's scalar polynomial methods, Bernoulli's method, and eigenvector powering.
Abstract: : A matrix S is a solvent of the matrix polynomial M(X) identically equal to X sup m + A(sub 1) X sup(M - 1) + + A sub m, if M(S) = 0, where A sub i, X and S are square matrices The authors present some new mathematical results for matrix polynomials, as well as a globally convergent algorithm for calculating such solvents In the theoretical part of this paper, existence theorems for solvents, a generalized division, interpolation, a block Vandermonde, and a generalized Lagrangian basis are studied Algorithms are presented which generalize Traub's scalar polynomial methods, Bernoulli's method, and eigenvector powering The related lambda-matrix problem, that of finding a scalar lambda such that I(lambda sup m) + A(sub 1)lambda sup(M - 1) + + A sup m is singular, is examined along with the matrix polynomial problem The matrix polynomial problem can be cast into a block eigenvalue formulation as follows Given a matrix A of order mn, find a matrix X of order n, such that AV = VX, where V is a matrix of full rank Some of the implications of this new block eigenvalue formulation are considered
21 citations