Recently, there has been a great deal of interest in the construction of exponential
integrators. These integrators, as their name suggests, use the exponential function (and …

The ubiquity of semilinear parabolic equations is clear from their numerous applications
ranging from physics and biology to materials and social sciences. In this paper, we …

The title of this book, Matria: Iterative Analysis, suggests that we might consider here all
matrix numerical methods which are iterative in nature. However, such an ambitious goal is …

This book evolved from lecture notes developed over the past 20+ years of teaching this
material, mostly in Applied Mathematics 585–6 at the University of Washington. The course …

Functions of matrices have been studied for as long as matrix algebra itself. Indeed, in his
seminal A Memoir on the Theory of Matrices (1858), Cayley investigated the square root of a …

In principle, the exponential of a matrix could be computed in many ways. Methods involving
approximation theory, differential equations, the matrix eigenvalues, and the matrix …

In this paper we consider the construction, analysis, implementation and application of
exponential integrators. The focus will be on two types of stiff problems. The first one is …

We present a collection of methods to simulate entangled dynamics of open quantum
systems governed by the Lindblad master equation with tensor network methods. Tensor …

Based on extensive research by Henk van der Vorst, this book presents an overview of a
number of Krylov projection methods for the solution of linear systems of equations. Van der …

Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it
computes either a small matrix exponential in full, the action of a large sparse matrix …