Simultaneous Similarity Reductions for a Pair of Matrices to Condensed Forms

Ren Cang Li; Qiang Ye

doi:10.1007/s40304-014-0033-y

Simultaneous Similarity Reductions for a Pair of Matrices to Condensed Forms

Ren Cang Li
, Qiang Ye

Producción científica: Article › revisión exhaustiva

3 Citas (Scopus)

Resumen

We present simultaneous reduction algorithms for two (nonsymmetric) matrices A and B to upper Hessenberg and lower Hessenberg forms, respectively. One is through the simultaneous similarity reduction and the other is through a Lanczos–Arnoldi-type iteration. The algorithm that uses the Lanczos–Arnoldi-type iteration can be considered as a generalization of both the nonsymmetric Lanczos algorithm and the standard Arnoldi algorithm. We shall also apply our reduction to construct a model reduction for certain kind second-order single-input single-output system. It is proved that the model reduction has the desirable moment matching property.

Idioma original	English
Páginas (desde-hasta)	139-153
Número de páginas	15
Publicación	Communications in Mathematics and Statistics
Volumen	2
N.º	2
DOI	https://doi.org/10.1007/s40304-014-0033-y
Estado	Published - jun 1 2014

Nota bibliográfica

Publisher Copyright:
© 2014, School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag Berlin Heidelberg.

Financiación

Acknowledgments Research of R. Li is supported in part by NSF grants DMS-1115834 and DMS-1317330, and a Research Gift Grant from Intel Corporation. Research of Q. Ye is supported in part by NSF Grants DMS–1318633 and DMS-1317424.

Financiadores	Número del financiador
National Science Foundation (NSF)	DMS-1317330, DMS-1115834, 1318633, 1317424
Intel Corporation	DMS–1318633, DMS-1317424

ASJC Scopus subject areas

Statistics and Probability
Computational Mathematics
Applied Mathematics

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title = "Simultaneous Similarity Reductions for a Pair of Matrices to Condensed Forms",

abstract = "We present simultaneous reduction algorithms for two (nonsymmetric) matrices A and B to upper Hessenberg and lower Hessenberg forms, respectively. One is through the simultaneous similarity reduction and the other is through a Lanczos–Arnoldi-type iteration. The algorithm that uses the Lanczos–Arnoldi-type iteration can be considered as a generalization of both the nonsymmetric Lanczos algorithm and the standard Arnoldi algorithm. We shall also apply our reduction to construct a model reduction for certain kind second-order single-input single-output system. It is proved that the model reduction has the desirable moment matching property.",

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AU - Li, Ren Cang

AU - Ye, Qiang

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N2 - We present simultaneous reduction algorithms for two (nonsymmetric) matrices A and B to upper Hessenberg and lower Hessenberg forms, respectively. One is through the simultaneous similarity reduction and the other is through a Lanczos–Arnoldi-type iteration. The algorithm that uses the Lanczos–Arnoldi-type iteration can be considered as a generalization of both the nonsymmetric Lanczos algorithm and the standard Arnoldi algorithm. We shall also apply our reduction to construct a model reduction for certain kind second-order single-input single-output system. It is proved that the model reduction has the desirable moment matching property.

AB - We present simultaneous reduction algorithms for two (nonsymmetric) matrices A and B to upper Hessenberg and lower Hessenberg forms, respectively. One is through the simultaneous similarity reduction and the other is through a Lanczos–Arnoldi-type iteration. The algorithm that uses the Lanczos–Arnoldi-type iteration can be considered as a generalization of both the nonsymmetric Lanczos algorithm and the standard Arnoldi algorithm. We shall also apply our reduction to construct a model reduction for certain kind second-order single-input single-output system. It is proved that the model reduction has the desirable moment matching property.

KW - Krylov subspace method

KW - Lanczos–Arnoldi iteration

KW - Model reduction

KW - Simultaneous reductions

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SP - 139

EP - 153

JO - Communications in Mathematics and Statistics

JF - Communications in Mathematics and Statistics

IS - 2

ER -

Simultaneous Similarity Reductions for a Pair of Matrices to Condensed Forms

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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