We introduce a new algorithm for approximation by rational functions on a real or complex
set of points, implementable in 40 lines of MATLAB and requiring no user input parameters …

A new rational Krylov method for the efficient solution of nonlinear eigenvalue problems,
A(λ)x=0, is proposed. This iterative method, called fully rational Krylov method for nonlinear …

When using the Arnoldi method for approximating f(A)\mathbfb, the action of a matrix
function on a vector, the maximum number of iterations that can be performed is often limited …

The computation of, the action of a matrix function on a vector, is a task arising in many
areas of scientific computing. In many applications, the matrix is sparse but so large that only …

A new construction of an absorbing boundary condition for indefinite Helmholtz problems on
unbounded domains is presented. This construction is based on a near-best uniform rational …

We present decay bounds for completely monotonic functions of Hermitian matrices, where
the matrix argument is banded or a Kronecker sum of banded matrices. This class includes …

Many important problems in mathematics and physics lead to (non-sparse) functions,
vectors, or matrices in which the fraction of nonnegligible entries is vanishingly small …

Evaluating the action of a matrix function on a vector, that is x= f (M) vx= f (M) v, is an
ubiquitous task in applications. When MM is large, one usually relies on Krylov projection …

Given a limited amount of memory and a target accuracy, we propose and compare several
polynomial Krylov methods for the approximation of f(A)b, the action of a Stieltjes matrix …

This work develops novel rational Krylov methods for updating a large-scale matrix function
f(A) when A is subject to low-rank modifications. It extends our previous work in this context …