Fast enclosure for the minimum norm least squares solution of the matrix equation AXB = C

SummaryFast algorithms for enclosing the minimum norm least squares solution of the matrix equation AXB = C are proposed. To develop these algorithms, theories for obtaining error bounds of numerical solutions are established. The error bounds obtained by these algorithms are verified in the sense t...

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Bibliographic Details
Published inNumerical linear algebra with applications Vol. 22; no. 3; pp. 548 - 563
Main Author Miyajima, Shinya
Format Journal Article
LanguageEnglish
Published Oxford Blackwell Publishing Ltd 01.05.2015
Wiley Subscription Services, Inc
Subjects
Algorithms
Enclosure
Error detection
Errors
Least squares method
least squares solution
Linear algebra
Mathematical analysis
Mathematical models
matrix equation
Moore-Penrose inverse
Norms
numerical enclosure
verified computation
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Summary:SummaryFast algorithms for enclosing the minimum norm least squares solution of the matrix equation AXB = C are proposed. To develop these algorithms, theories for obtaining error bounds of numerical solutions are established. The error bounds obtained by these algorithms are verified in the sense that all the possible rounding errors have been taken into account. Techniques for accelerating the enclosure and obtaining smaller error bounds are introduced. Numerical results show the properties of the proposed algorithms. Copyright © 2015 John Wiley & Sons, Ltd.
Bibliography:ArticleID:NLA1971
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SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.1971