Fast verification for all eigenpairs in symmetric positive definite generalized eigenvalue problems

Shinya Miyajima; Takeshi Ogita; Siegfried M. Rump; Shin'ichi Oishi

Fast verification for all eigenpairs in symmetric positive definite generalized eigenvalue problems

Shinya Miyajima, Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi

School of Fundamental Science and Engineering

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

16 Citations (Scopus)

Abstract

A fast method for enclosing all eigenpairs in symmetric positive definite generalized eigenvalue problems is proposed. Firstly theorems on verifying all eigenvalues are presented. Next a theorem on verifying all eigenvectors is presented. The proposed method is developed based on these theorems. Numerical results are presented showing the efficiency of the proposed method. As an application of the proposed method, an efficient method of enclosing all eigenpairs in the quadratic eigenvalue problem is also sketched.

Original language	English
Pages (from-to)	24-45
Number of pages	22
Journal	Reliable Computing
Volume	14
Publication status	Published - 2010 Jun 1

Keywords

Eigenpairs
Generalized eigenvalue problem
Numerical verification

ASJC Scopus subject areas

Software
Computational Mathematics
Applied Mathematics

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abstract = "A fast method for enclosing all eigenpairs in symmetric positive definite generalized eigenvalue problems is proposed. Firstly theorems on verifying all eigenvalues are presented. Next a theorem on verifying all eigenvectors is presented. The proposed method is developed based on these theorems. Numerical results are presented showing the efficiency of the proposed method. As an application of the proposed method, an efficient method of enclosing all eigenpairs in the quadratic eigenvalue problem is also sketched.",

keywords = "Eigenpairs, Generalized eigenvalue problem, Numerical verification",

author = "Shinya Miyajima and Takeshi Ogita and Rump, {Siegfried M.} and Shin'ichi Oishi",

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AU - Miyajima, Shinya

AU - Ogita, Takeshi

AU - Rump, Siegfried M.

AU - Oishi, Shin'ichi

PY - 2010/6/1

Y1 - 2010/6/1

N2 - A fast method for enclosing all eigenpairs in symmetric positive definite generalized eigenvalue problems is proposed. Firstly theorems on verifying all eigenvalues are presented. Next a theorem on verifying all eigenvectors is presented. The proposed method is developed based on these theorems. Numerical results are presented showing the efficiency of the proposed method. As an application of the proposed method, an efficient method of enclosing all eigenpairs in the quadratic eigenvalue problem is also sketched.

AB - A fast method for enclosing all eigenpairs in symmetric positive definite generalized eigenvalue problems is proposed. Firstly theorems on verifying all eigenvalues are presented. Next a theorem on verifying all eigenvectors is presented. The proposed method is developed based on these theorems. Numerical results are presented showing the efficiency of the proposed method. As an application of the proposed method, an efficient method of enclosing all eigenpairs in the quadratic eigenvalue problem is also sketched.

KW - Eigenpairs

KW - Generalized eigenvalue problem

KW - Numerical verification

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JF - Reliable Computing

SN - 1385-3139

ER -

Fast verification for all eigenpairs in symmetric positive definite generalized eigenvalue problems

Abstract

Keywords

ASJC Scopus subject areas

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