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Computing AAlpha, log(A), and Related Matrix Functions by Contour Integrals.

Abstract:

New methods are proposed for the numerical evaluation of f(A) or f(A)b, where f(A) is a function such as A1/2 or log(A) with singularities in (-∞, 0] and A is a matrix with eigenvalues on or near (0, ∞). The methods are based on combining contour integrals evaluated by the periodic trapezoid rule with conformal maps involving Jacobi elliptic functions. The convergence is geometric, so that the computation of f(A)fe is typically reduced to one or two dozen linear system solves, which can be ca...

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Publication status:
Published

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Publisher copy:
10.1137/070700607

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
SIAM J. Numerical Analysis
Volume:
46
Issue:
5
Pages:
2505-2523
Publication date:
2008-01-01
DOI:
EISSN:
1095-7170
ISSN:
0036-1429
Source identifiers:
188993
Language:
English
Keywords:
Pubs id:
pubs:188993
UUID:
uuid:6f50f9c3-34f8-4ac4-a23f-93f93496d22c
Local pid:
pubs:188993
Deposit date:
2012-12-19

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