Block power method for computing solvents and spectral factors of matrix polynomials

Jason Sheng-Hon Tsai, L. S. Shieh, T. T.C. Shen

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

This paper is concerned with the extension of the power method, used for finding the largest eigenvalue and associated eigenvector of a matrix, to its block from for computing the largest block eigenvalue and associated block eigenvector of a non-symmetric matrix. Based on the developed block power method, several algorithms are developed for solving the complete set of solvents and spectral factors of a matrix polynomial, without prior knowledge of the latent roots of the matrix polynomial. Moreover, when any right/left solvent of a matrix polynomial is given, the proposed method can be used to determine the corresponding left/right solvent such that both right and left solvents have the same eigenspectra. The matrix polynomial of interest must have distinct block solvents and a corresponding non-singular polynomial matrix. The established algorithms can be applied in the analysis and/or design of systems described by high-degree vector differential equations and/or matrix fraction descriptions.

Original languageEnglish
Pages (from-to)683-699
Number of pages17
JournalComputers and Mathematics with Applications
Volume16
Issue number9
DOIs
Publication statusPublished - 1988 Jan 1

Fingerprint

Power Method
Block Method
Matrix Polynomial
Polynomials
Computing
Eigenvector
Latent Root
Nonsymmetric Matrix
Polynomial Matrices
Eigenvalues and eigenfunctions
Largest Eigenvalue
Prior Knowledge
Differential equation
Eigenvalue
Distinct
Differential equations

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

Cite this

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Block power method for computing solvents and spectral factors of matrix polynomials. / Tsai, Jason Sheng-Hon; Shieh, L. S.; Shen, T. T.C.

In: Computers and Mathematics with Applications, Vol. 16, No. 9, 01.01.1988, p. 683-699.

Research output: Contribution to journalArticle

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