Generalized rational Krylov decompositions are matrix relations which, under certain
conditions, are associated with rational Krylov spaces. We study the algebraic properties of …

We consider the problem of approximating the von Neumann entropy of a large, sparse,
symmetric positive semidefinite matrix A, defined as tr (f (A)) where f (x)=-x log x. After …

This paper is concerned with computing approximations of matrix functionals of the form F
(A):= v T f (A) v, where A is a large symmetric positive definite matrix, v is a vector, and f is a …

Rational Krylov subspaces have become a reference tool in dimension reduction
procedures for several application problems. When data matrices are symmetric, a short …

Numerical methods based on rational Krylov spaces have become an indispensable tool of
scientific computing. In this thesis we study rational Krylov spaces by considering rational …

Many applications in physics and network science require the computation of quantities
related to certain matrix functions. In many cases, a straightforward way to proceed is by …

This paper considers the computation of approximations of matrix functionals of form F (A):=
v T f (A) v, where A is a large symmetric positive definite matrix, v is a vector, and f is a …

We present a numerical procedure to approximate integrals of the form∫ baf (x) dx, where f
is a function with singularities close to, but outside the interval [a, b], with−∞⊠ a< b⊠+∞. The …

This article deduces geometric convergence rates for approximating matrix functions via
inverse-free rational Krylov methods. In applications one frequently encounters matrix …

This paper is concerned with the approximation of matrix functionals of the form w T f (A) v,
where A∈ ℝ n× n A∈R^n*n is a large nonsymmetric matrix, w, v∈ ℝ nw,v∈R^n, and f is a …