### 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 language | English |
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Pages (from-to) | 211-235 |

Number of pages | 25 |

Journal | Applied Mathematics and Computation |

Volume | 47 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - 1992 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Computational Mathematics
- Applied Mathematics

### Cite this

*Applied Mathematics and Computation*,

*47*(2-3), 211-235. https://doi.org/10.1016/0096-3003(92)90048-6

}

*Applied Mathematics and Computation*, vol. 47, no. 2-3, pp. 211-235. https://doi.org/10.1016/0096-3003(92)90048-6

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - A computer-aided method for solvents and spectral factors of matrix polynomials

AU - Tsai, Jason Sheng-Hon

AU - Chen, C. M.

AU - Shieh, L. S.

PY - 1992/1/1

Y1 - 1992/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=38249013831&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249013831&partnerID=8YFLogxK

U2 - 10.1016/0096-3003(92)90048-6

DO - 10.1016/0096-3003(92)90048-6

M3 - Article

VL - 47

SP - 211

EP - 235

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 2-3

ER -