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 …

Krylov subspace methods for approximating the action of matrix exponentials are analyzed
in this paper. We derive error bounds via a functional calculus of Arnoldi and Lanczos …

A new class of exponential propagation techniques which we call exponential propagation
iterative (EPI) methods is introduced in this paper. It is demonstrated how for large stiff …

Restricted Denominator (RD) rational approximations to the matrix exponential operator are
constructed by interpolation in points related to Krylov subspaces associated to a rational …

The need to evaluate expressions of the form f(A) or f(A)b, where f is a nonlinear function, A
is a large sparse n*n matrix, and b is an n-vector, arises in many applications. This paper …

A novel parallel algorithm for the integration of linear initial-value problems is proposed. This
algorithm is based on the simple observation that homogeneous problems can typically be …

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 …

In this article we investigate model order reduction of large-scale systems using time-limited
balanced truncation, which restricts the well known balanced truncation framework to …

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 …