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 08:04 
Last Modified:  29 May 2015 18:46 
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