Approximate Diagonalization

We describe a new method of computing functions of highly nonnormal matrices by using the concept of approximate diagonalization. We formulate a conjecture about its efficiency and provide both theoretical and numerical evidence in support of the conjecture. We apply the method to compute arbitrary...

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Vydáno v:SIAM journal on matrix analysis and applications Ročník 29; číslo 4; s. 1051 - 1064
Hlavní autor: Davies, E. B.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2007
Témata:
Accuracy
Algebra
Eigenvalues
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Numerical linear algebra
Operator theory
Sciences and techniques of general use
Diagonalization
Support
fractional powers
ill-posedness
Jordan matrices
spectral theory; 65F22
47A52
47A60
Regularization method
15A42
functional calculus
Numerical analysis
Spectral theory
Efficiency
Linear algebra
Fractional power
65F15
Matrices
Ill posed problem
15A60
Computing method
Regularization
ISSN:0895-4798, 1095-7162
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Shrnutí:We describe a new method of computing functions of highly nonnormal matrices by using the concept of approximate diagonalization. We formulate a conjecture about its efficiency and provide both theoretical and numerical evidence in support of the conjecture. We apply the method to compute arbitrary real powers of highly nonnormal matrices.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0895-4798
1095-7162
DOI:10.1137/060659909