Error estimates for the approximate computation of matrix functions
Event details
| Date | 21.12.2011 |
| Hour | 16:15 |
| Speaker | Dr. Bernhard Beckermann |
| Location |
CM013
|
| Category | Conferences - Seminars |
An important problem arising in science 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 sufficiently smooth
function, 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 Krylov or rational Krylov spaces, which mathematically is equivalent to
interpolate f by some rational functions with fixed poles, and interpolation points given by so-called rational Ritz values. Following recent work of Crouzeix, we will present some numerical range error estimates, leading to linear convergence rates. In the case of hermitian (sequences of) matrices coming for instance from the semi-discretisation of the heat equation, we present another asymptotic error estimate leading to superlinear convergence. Partly joint work with L. Reichel (Kent) and S. Güttel (Oxford).
Links
Practical information
- General public
- Free
Contact
- Prof. Daniel Kressner