A computer-aided method for solvents and spectral factors of matrix polynomials

Jason Sheng-Hon Tsai, C. M. Chen, L. S. Shieh

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

A new approach for determining the complete sets of solvents and spectral factors of a monic matrix polynomial is proposed. A systematic method for determining the initial guess for the extended multidimensional Newton-Raphson method is first proposed, such that the eigenspectrum corresponding to each solvent of the matrix polynomial can be determined. With the evaluated eigenspectra, complete sets of solvents and spectral factors of a monic matrix polynomial can be obtained by utilizing the applications and the advantages of the principal-nth-root method, the matrix sign function, and the block-power method. The established algorithms can be applied in the analysis and/or design of systems described by high-degree vector differential equations and/or matrix fractions.

Original languageEnglish
Pages (from-to)211-235
Number of pages25
JournalApplied Mathematics and Computation
Volume47
Issue number2-3
DOIs
Publication statusPublished - 1992 Jan 1

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Matrix Polynomial
Monic polynomial
Polynomials
Matrix Sign Function
nth root
Power Method
Newton-Raphson method
Block Method
Guess
Differential equation
Differential equations

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

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A computer-aided method for solvents and spectral factors of matrix polynomials. / Tsai, Jason Sheng-Hon; Chen, C. M.; Shieh, L. S.

In: Applied Mathematics and Computation, Vol. 47, No. 2-3, 01.01.1992, p. 211-235.

Research output: Contribution to journalArticle

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