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

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

*この研究の対応する著者

研究成果: Article査読

17 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)24-45
ページ数22
ジャーナルReliable Computing
14
出版ステータスPublished - 2010 6月 1

ASJC Scopus subject areas

  • ソフトウェア
  • 計算数学
  • 応用数学

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