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

J. S.H. Tsai, L. S. Shieh, T. T.C. Shen

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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
Issue number9
Publication statusPublished - 1988

All Science Journal Classification (ASJC) codes

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


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