TY - JOUR

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

AU - Tsai, J. S.H.

AU - Chen, C. M.

AU - Shieh, L. S.

N1 - Funding Information:
*This work was supported in part by the National Science Council of the Republic of China under contract NSC-80-0404-E-006-48, the NASA-Johnson Space Center under grant NAG-9-380, and the U. S. Army Research Ofice under grant DAAL-03-91-G-0106.

PY - 1992/2

Y1 - 1992/2

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.

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

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

M3 - Article

AN - SCOPUS:38249013831

SN - 0096-3003

VL - 47

SP - 211

EP - 235

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 2-3

ER -