Author
Hale, N
Higham, N
Trefethen, L
Journal title
SIAM Journal on Numerical Analysis
DOI
10.1137/070700607
Issue
5
Volume
46
Last updated
2021-10-19T13:19:23.727+01:00
Page
2505-2523
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 carried out in parallel. © 2008 Society for Industrial and Applied Mathematics.
Symplectic ID
188993
Favourite
On
Publication type
Journal Article
Publication date
10 Nov 2008
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