The eigenvalues of preconditioned matrices for linear multistep formulas in boundary value form

Daniele Bertaccini; Youwei Wen; Michael K. Ng

doi:10.1002/nla.419

The eigenvalues of preconditioned matrices for linear multistep formulas in boundary value form

Daniele Bertaccini^*, Youwei Wen, Michael K. Ng

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

1 Citation (Scopus)

Abstract

The application of linear multistep formulas in boundary value form for the solutions of initial and boundary value problems requires the solutions of linear systems of which the coefficient matrices are large and sparse block-Toeplitz-like matrices. Block-circulant preconditioners applied to these linear systems are examined. Analytical formulas for the eigenvalues of these preconditioned matrices are derived. The eigenvalues are also predicted by an asymptotic analysis.

Original language	English
Pages (from-to)	315-325
Number of pages	11
Journal	Numerical Linear Algebra with Applications
Volume	12
Issue number	2-3
DOIs	https://doi.org/10.1002/nla.419
Publication status	Published - Mar 2005

Scopus Subject Areas

Algebra and Number Theory
Applied Mathematics

User-Defined Keywords

Circulant matrices
Eigenvalues
Linear multistep formulas in bv form
Non-symmetric Toeplitz matrices

Access to Document

10.1002/nla.419

Cite this

@article{8099bd5e10084a3f902e725ed0a686b7,

title = "The eigenvalues of preconditioned matrices for linear multistep formulas in boundary value form",

abstract = "The application of linear multistep formulas in boundary value form for the solutions of initial and boundary value problems requires the solutions of linear systems of which the coefficient matrices are large and sparse block-Toeplitz-like matrices. Block-circulant preconditioners applied to these linear systems are examined. Analytical formulas for the eigenvalues of these preconditioned matrices are derived. The eigenvalues are also predicted by an asymptotic analysis.",

keywords = "Circulant matrices, Eigenvalues, Linear multistep formulas in bv form, Non-symmetric Toeplitz matrices",

author = "Daniele Bertaccini and Youwei Wen and Ng, {Michael K.}",

note = "Funding Information: Italian Ministry of Scientific Research GNCS-INdAM Natural Science Foundation of China. Grant Number: 19971018 RGC. Grant Number: 7132/00P RGC. Grant Number: 7130/02P HKU CRCG. Grant Number: 10203501 HKU CRCG. Grant Number: 10203907 HKU CRCG. Grant Number: 10203408 Publisher copyright: {\textcopyright} 2004 John Wiley & Sons, Ltd.",

year = "2005",

month = mar,

doi = "10.1002/nla.419",

language = "English",

volume = "12",

pages = "315--325",

journal = "Numerical Linear Algebra with Applications",

issn = "1070-5325",

publisher = "John Wiley & Sons Ltd.",

number = "2-3",

}

TY - JOUR

T1 - The eigenvalues of preconditioned matrices for linear multistep formulas in boundary value form

AU - Bertaccini, Daniele

AU - Wen, Youwei

AU - Ng, Michael K.

N1 - Funding Information: Italian Ministry of Scientific Research GNCS-INdAM Natural Science Foundation of China. Grant Number: 19971018 RGC. Grant Number: 7132/00P RGC. Grant Number: 7130/02P HKU CRCG. Grant Number: 10203501 HKU CRCG. Grant Number: 10203907 HKU CRCG. Grant Number: 10203408 Publisher copyright: © 2004 John Wiley & Sons, Ltd.

PY - 2005/3

Y1 - 2005/3

N2 - The application of linear multistep formulas in boundary value form for the solutions of initial and boundary value problems requires the solutions of linear systems of which the coefficient matrices are large and sparse block-Toeplitz-like matrices. Block-circulant preconditioners applied to these linear systems are examined. Analytical formulas for the eigenvalues of these preconditioned matrices are derived. The eigenvalues are also predicted by an asymptotic analysis.

AB - The application of linear multistep formulas in boundary value form for the solutions of initial and boundary value problems requires the solutions of linear systems of which the coefficient matrices are large and sparse block-Toeplitz-like matrices. Block-circulant preconditioners applied to these linear systems are examined. Analytical formulas for the eigenvalues of these preconditioned matrices are derived. The eigenvalues are also predicted by an asymptotic analysis.

KW - Circulant matrices

KW - Eigenvalues

KW - Linear multistep formulas in bv form

KW - Non-symmetric Toeplitz matrices

UR - http://www.scopus.com/inward/record.url?scp=20744441827&partnerID=8YFLogxK

U2 - 10.1002/nla.419

DO - 10.1002/nla.419

M3 - Journal article

AN - SCOPUS:20744441827

SN - 1070-5325

VL - 12

SP - 315

EP - 325

JO - Numerical Linear Algebra with Applications

JF - Numerical Linear Algebra with Applications

IS - 2-3

ER -

The eigenvalues of preconditioned matrices for linear multistep formulas in boundary value form

Abstract

Scopus Subject Areas

User-Defined Keywords

Access to Document

Other files and links

Fingerprint

Cite this