Schmelzer, Thomas and Trefethen, Lloyd N. (2006) Evaluating matrix functions for exponential integrators via CarathéodoryFejér approximation and contour integrals. Technical Report. Unspecified. (Submitted)

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Abstract
Among the fastest methods for solving stiff PDE are exponential integrators, which require the evaluation of , where is a negative definite matrix and is the exponential function or one of the related `` functions'' such as . Building on previous work by Trefethen and Gutknecht, Gonchar and Rakhmanov, and Lu, we propose two methods for the fast evaluation of that are especially useful when shifted systems can be solved efficiently, e.g. by a sparse direct solver. The first method method is based on best rational approximations to on the negative real axis computed via the CarathéodoryFejér procedure, and we conjecture that the accuracy scales as , where is the number of complex matrix solves. In particular, three matrix solves suffice to evaluate to approximately six digits of accuracy. The second method is an application of the trapezoid rule on a Talbottype contour.
Item Type:  Technical Report (Technical Report) 

Subjects:  A  C > Approximations and expansions D  G > Functions of a complex variable H  N > Numerical analysis 
Research Groups:  Numerical Analysis Group 
ID Code:  1103 
Deposited By:  Lotti Ekert 
Deposited On:  11 May 2011 09:59 
Last Modified:  29 May 2015 18:47 
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