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

Solving systems of algebraic linear equations is among the most frequent problems in
scientific computing. It appears in many areas like physics, engineering, chemistry, biology …

A Journey through the History of Numerical Linear Algebra: Back Matter Page 1 Bibliography
[1] A. Abdelfattah, H. Anzt, A. Bouteiller, A. Danalis, JJ Dongarra, M. Gates, A. Haidar, J. Kurzak …

The block version of the rational Arnoldi method is a widely used procedure for generating
an orthonormal basis of a block rational Krylov space. We study block rational Arnoldi …

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 …

We propose a rational QZ method for the solution of the dense, unsymmetric generalized
eigenvalue problem. This generalization of the classical QZ method operates implicitly on a …

We present a class of algorithms based on rational Krylov methods to compute the action of
a generalized matrix function on a vector. These algorithms incorporate existing methods …

A general framework for oblique projections of non-Hermitian matrices onto rational Krylov
subspaces is developed. To obtain this framework we revisit the classical rational Krylov …

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 …