Approximation of functions of large matrices with Kronecker structure [article]

Michele Benzi, Valeria Simoncini
2015 arXiv   pre-print
We consider the numerical approximation of f( A)b where b∈ R^N and A is the sum of Kronecker products, that is A=M_2 ⊗ I + I ⊗ M_1∈ R^N× N. Here f is a regular function such that f( A) is well defined. We derive a computational strategy that significantly lowers the memory requirements and computational efforts of the standard approximations, with special emphasis on the exponential function, for which the new procedure becomes particularly advantageous. Our findings are illustrated by
more » ... experiments with typical functions used in applications.
arXiv:1503.02615v1 fatcat:agko7bdxgnhbrfnvquc2qkqlsq