### 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 language | English |
---|---|

Pages (from-to) | 683-699 |

Number of pages | 17 |

Journal | Computers and Mathematics with Applications |

Volume | 16 |

Issue number | 9 |

DOIs | |

Publication status | Published - 1988 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics

### Cite this

*Computers and Mathematics with Applications*,

*16*(9), 683-699. https://doi.org/10.1016/0898-1221(88)90004-1

}

*Computers and Mathematics with Applications*, vol. 16, no. 9, pp. 683-699. https://doi.org/10.1016/0898-1221(88)90004-1

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Block power method for computing solvents and spectral factors of matrix polynomials

AU - Tsai, Jason Sheng-Hon

AU - Shieh, L. S.

AU - Shen, T. T.C.

PY - 1988/1/1

Y1 - 1988/1/1

N2 - 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.

AB - 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.

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U2 - 10.1016/0898-1221(88)90004-1

DO - 10.1016/0898-1221(88)90004-1

M3 - Article

VL - 16

SP - 683

EP - 699

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 9

ER -