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

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English
Pages (from-to)	139-153
Number of pages	15
Journal	Communications in Mathematics and Statistics
Volume	2
Issue number	2
DOIs	https://doi.org/10.1007/s40304-014-0033-y
State	Published - Jun 1 2014

Bibliographical note

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

Keywords

Krylov subspace method
Lanczos–Arnoldi iteration
Model reduction
Simultaneous reductions

ASJC Scopus subject areas

Statistics and Probability
Computational Mathematics
Applied Mathematics

Access to Document

10.1007/s40304-014-0033-y

Cite this

@article{e32b49d26efe4199a6335e989a62fc8a,

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.",

keywords = "Krylov subspace method, Lanczos–Arnoldi iteration, Model reduction, Simultaneous reductions",

author = "Li, {Ren Cang} and Qiang Ye",

note = "Publisher Copyright: {\textcopyright} 2014, School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag Berlin Heidelberg.",

year = "2014",

month = jun,

day = "1",

doi = "10.1007/s40304-014-0033-y",

language = "English",

volume = "2",

pages = "139--153",

number = "2",

}

TY - JOUR

T1 - Simultaneous Similarity Reductions for a Pair of Matrices to Condensed Forms

AU - Li, Ren Cang

AU - Ye, Qiang

PY - 2014/6/1

Y1 - 2014/6/1

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

UR - http://www.scopus.com/inward/record.url?scp=84976340234&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84976340234&partnerID=8YFLogxK

U2 - 10.1007/s40304-014-0033-y

DO - 10.1007/s40304-014-0033-y

M3 - Article

AN - SCOPUS:84976340234

SN - 2194-6701

VL - 2

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this