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.


Get started

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