Randomized sketching for Krylov approximations of large-scale matrix functions

Understand

The computation of f(A)b, the action of a matrix function on a vector, is a task arising in many areas of scientific computing.

• In many applications, the matrix A is sparse but so large that only a rather small number of Krylov basis vectors can be stored.
• Here we discuss a new approach to overcome these limitations by randomized sketching combined with an integral representation of f(A)b.
• Two different approximations are introduced, one based on sketched FOM and another based on sketched GMRES approximation.