Many advances in the development of Krylov subspace methods for the iterative solution of
linear systems during the last decade and a half are reviewed. These new developments …

This computationally oriented book describes and explains the mathematical relationships
among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and …

The Lanczos and conjugate gradient algorithms were introduced more than five decades
ago as tools for numerical computation of dominant eigenvalues of symmetric matrices and …

The Lanczos algorithm is one of the most frequently used numerical methods for computing
a few eigenvalues (and eventually eigenvectors) of a large sparse symmetric matrix A. If the …

In their paper published in 1952, Hestenes and Stiefel considered the conjugate gradient
(CG) method an iterative method which terminates in at most n steps if no rounding errors …

For the finite volume discretization of a second-order elliptic model problem, we derive a
posteriori error estimates which take into account an inexact solution of the associated linear …

Summary The Conjugate Gradient method has always been successfully used in solving the
symmetric and positive definite systems obtained by the finite element approximation of self …

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 …

This paper presents a methodology for computing upper and lower bounds for both the
algebraic and total errors in the context of the conforming finite element discretization of the …

We consider a family of practical stopping criteria for linear solvers for adaptive finite
element methods for symmetric elliptic problems. A contraction property between two …