4 papers
A low-memory Lanczos method with rational Krylov compression for matrix functions
Angelo A. Casulli, Igor Simunec
In this work we introduce a memory-efficient method for computing the action of a Hermitian matrix function on a vector. Our method consists of a rational Lanczos algorithm combine…
Error bounds for the approximation of matrix functions with rational Krylov methods
Igor Simunec
We obtain an expression for the error in the approximation of and with rational Krylov methods, where is a symmetri…
A sketch-and-select Arnoldi process
Stefan Güttel, Igor Simunec
A sketch-and-select Arnoldi process to generate a well-conditioned basis of a Krylov space at low cost is proposed. At each iteration the procedure utilizes randomized sketching to…
Computation of generalized matrix functions with rational Krylov methods
Angelo Alberto Casulli, Igor Simunec
We present a class of algorithms based on rational Krylov methods to compute the action of a generalized matrix function on a vector. These algorithms incorporate existing methods…