Fast enclosure of matrix eigenvalues and singular values via rounding mode controlled computation

研究成果: Article

18 引用 (Scopus)

抄録

Modifications of Bauer-Fike type and Weyl type perturbation theorems are presented for matrix eigenvalue and singular value problems. It is shown that the conditions of the presented theorems can be rigorously checked by floating point computation with rounding mode control. It is stressed that verification programs can be easily constructed on usual numerical softwares like MATLAB. Computational cost of obtaining rigorous error bounds for computed eigenvalues is shown to be 6n3 flops for a real symmetric n×n matrix.

元の言語English
ページ(範囲)133-146
ページ数14
ジャーナルLinear Algebra and Its Applications
324
発行部数1-3
DOI
出版物ステータスPublished - 2001 2 15
外部発表Yes

Fingerprint

Rounding
Enclosure
Singular Values
Enclosures
Eigenvalue
Program Verification
Floating point
Symmetric matrix
Theorem
Error Bounds
MATLAB
Computational Cost
Perturbation
Software
Costs

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis

これを引用

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AB - Modifications of Bauer-Fike type and Weyl type perturbation theorems are presented for matrix eigenvalue and singular value problems. It is shown that the conditions of the presented theorems can be rigorously checked by floating point computation with rounding mode control. It is stressed that verification programs can be easily constructed on usual numerical softwares like MATLAB. Computational cost of obtaining rigorous error bounds for computed eigenvalues is shown to be 6n3 flops for a real symmetric n×n matrix.

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KW - Weyl type theorem

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