The Mathematical Institute, University of Oxford, Eprints Archive

Computing Aα, log(A) and related matrix functions by contour integrals

Hale, Nicholas and Higham, Nicholas J. and Trefethen, Lloyd N. (2007) Computing Aα, log(A) and related matrix functions by contour integrals. Technical Report. Unspecified. (Submitted)

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Abstract

New methods are proposed for the numerical evaluation of f(A) or f(A) b, where f(A) is a function such as A½ 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)b is typically reduced to one or two dozen linear system solves, which can be carried out in parallel.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1085
Deposited By:Lotti Ekert
Deposited On:07 May 2011 09:04
Last Modified:07 May 2011 09:04

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