Geodesic
Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals
Electronic transactions on numerical analysis, Tome 29 (2008).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Among the fastest methods for solving stiff PDE are exponential integrators, which require the evaluation of , where is a negative semidefinite matrix and is the exponential function or one of the related $\sterling $########$${\S}$$###$\copyright \ddot $###$ \sterling $" functions" such as . Building on previous work by Trefethen and Gutknecht, Minchev, $$###$$§$\ddot $###§! #"%$!\ddot '\( and Lu, we propose two methods for the fast evaluation of that are especially useful when shifted systems $£$########$${\S}$$###$©ddot$can be solved efficiently, e.g. by a sparse direct solver. The first method is based on best rational $$###)###$$10132$ddot546$87 approximations to on the negative real axis computed via the Carath\'eodory-Fej\'er procedure. Rather than using $£$optimal poles we approximate the functions in a set of common poles, which speeds up typical computations by a factor of to . The second method is an application of the trapezoid rule on a Talbot-type contour.$
Classification : 65L05, 41A20, 30E20
Keywords: matrix exponential, exponential integrators, stiff semilinear parabolic pdes, rational uniform approximation, Hankel contour, numerical quadrature 
@article{ETNA_2008__29__a13,
     author = {Schmelzer, Thomas and Trefethen, Lloyd N.},
     title = {Evaluating matrix functions for exponential integrators via {Carath\'eodory-Fej\'er} approximation and contour integrals},
     journal = {Electronic transactions on numerical analysis},
     publisher = {mathdoc},
     volume = {29},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__29__a13/}
}
TY  - JOUR
AU  - Schmelzer, Thomas
AU  - Trefethen, Lloyd N.
TI  - Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals
JO  - Electronic transactions on numerical analysis
PY  - 2008
VL  - 29
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ETNA_2008__29__a13/
LA  - en
ID  - ETNA_2008__29__a13
ER  - 
%0 Journal Article
%A Schmelzer, Thomas
%A Trefethen, Lloyd N.
%T Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals
%J Electronic transactions on numerical analysis
%D 2008
%V 29
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ETNA_2008__29__a13/
%G en
%F ETNA_2008__29__a13
Schmelzer, Thomas; Trefethen, Lloyd N. Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals. Electronic transactions on numerical analysis, Tome 29 (2008). http://geodesic.mathdoc.fr/item/ETNA_2008__29__a13/