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 …

It has been shown that approximate extended Krylov subspaces can be computed, under
certain assumptions, without any explicit inversion or system solves. Instead, the vectors …

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 …

In inverse eigenvalue problems one tries to reconstruct a matrix, satisfying some constraints,
given some spectral information. Here, two inverse eigenvalue problems are solved. First …

In this paper we discuss the deflation criterion used in the extended QR algorithm based on
the chasing of rotations. We provide absolute and relative perturbation bounds for this …

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 …

Two inverse eigenvalue problems are discussed. First, given the eigenvalues and a weight
vector an extended Hessenberg matrix is computed. This matrix represents the recurrences …

An extended QR algorithm specifically tailored for Hamiltonian matrices is presented. The
algorithm generalizes the customary Hamiltonian QR algorithm with additional freedom in …