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PRODID:-//Memento EPFL//
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SUMMARY:Error estimates for the approximate computation of matrix function
 s
DTSTART:20111221T161500
DTSTAMP:20260408T044338Z
UID:472023229aabbf3a654f1a73988753e69c5cb34fc5c7aad0a5e54b4d
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dr. Bernhard Beckermann\nAn important problem arising in scien
 ce and engineering is the computation of matrix functions f(A)b\, where A 
 is a large Hermitian matrix\, b a vector of unit length\, and f is a suffi
 ciently smooth\nfunction\, e.g.\, A-1/2b with a Markov function f\, or f(z
 ) = exp(z). Here a popular method consists in projecting to so-called Kryl
 ov or rational Krylov spaces\, which mathematically is equivalent to\ninte
 rpolate f by some rational functions with fixed poles\, and interpolation 
 points given by so-called rational Ritz values. Following recent work of C
 rouzeix\, we will present some numerical range error estimates\, leading t
 o linear convergence rates. In the case of hermitian (sequences of) matric
 es coming for instance from the semi-discretisation of the heat equation\,
  we present another asymptotic error estimate leading to superlinear conve
 rgence. Partly joint work with L. Reichel (Kent) and S. Güttel (Oxford).
LOCATION:CM013
STATUS:CONFIRMED
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