This book started as a set of lectures in computational science for inverse problems where
electromagnetics was used as an example. Talking with many graduate students and other …

Matrix functions are a central topic of linear algebra, and problems of their numerical
approximation appear increasingly often in scientific computing. We review various rational …

We present a unified and self-contained treatment of rational Krylov methods for
approximating the product of a function of a linear operator with a vector. With the help of …

The need to evaluate a function f (A)∈ ℂn× n of a matrix A∈ ℂn× n arises in a wide and
growing number of applications, ranging from the numerical solution of differential equations …

For large square matrices A and functions f, the numerical approximation of the action of f (A)
to a vector v has received considerable attention in the last two decades. In this paper we …

We consider the computation of u(t)=\exp(-tA)φ using rational Krylov subspace reduction for
0≤t<∞, where u(t),φ∈R^N and 0<A=A^*∈R^N*N. The objective of this work is the …

A common problem in statistics is to compute sample vectors from a multivariate Gaussian
distribution with zero mean and a given covariance matrix A. A canonical approach to the …

We compute u(t)=\exp(-tA)φ using rational Krylov subspace reduction for 0≦t<∞, where
u(t),φ∈R^N and 0<A=A^*∈R^N*N. A priori optimization of the rational Krylov subspaces for …

The time-fractional Schrödinger equation is a fundamental topic in physics and its numerical
solution is still an open problem. Here we start from the possibility to express its solution by …

The main focus of this paper is the solution of some partial differential equations of fractional
order. Promising methods based on matrix functions are taken in consideration. The features …