Matlab implementation of a
black-box rational Arnoldi method
for Markov matrix functions
Rational Arnoldi is a powerful method for approximating a function f(z) of
large sparse matrix A times a vector v, namely f(A)v.
The selection of asymptotically
optimal parameters for this method is crucial for its fast convergence.
You may download the following Matlab code implementing a heuristic for the
automated pole selection when the function to be approximated is of
Markov-type, such as the matrix inverse square root or the matrix logarithm.
- Matlab files : markovfunmv.zip (right-click mouse, save link as...)
- Accompanying poster with references : poster.pdf
- Accompanying paper with references : paper.pdf (joint work with L. Knizhnerman)
We have implemented the matrix inverse square root
f = invsqrtmv(A,v);
and the matrix logarithm
f = logmv(A,v);
To get going, simply download the above zip archive, extract it, and
have a look at the included example files.
Please note that this is a research code and I am happy about critical comments.
In particular, it would be great to have relevant examples where the proposed
adaptive pole selection fails. Just send me an Email :
stefan at guettel dot com