Recent computational developments in Krylov subspace methods for linear systems

V Simoncini, DB Szyld - Numerical Linear Algebra with …, 2007 - Wiley Online Library
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 …

Numerical solution of saddle point problems

M Benzi, GH Golub, J Liesen - Acta numerica, 2005 - cambridge.org
Large linear systems of saddle point type arise in a wide variety of applications throughout
computational science and engineering. Due to their indefiniteness and often poor spectral …

[图书][B] Iterative Krylov methods for large linear systems

HA Van der Vorst - 2003 - books.google.com
Based on extensive research by Henk van der Vorst, this book presents an overview of a
number of Krylov projection methods for the solution of linear systems of equations. Van der …

GMRES algorithms over 35 years

Q Zou - Applied Mathematics and Computation, 2023 - Elsevier
This paper is about GMRES algorithms for the solution of nonsingular linear systems. We
first consider basic algorithms and study their convergence. We then focus on acceleration …

Modified Gram-Schmidt (MGS), least squares, and backward stability of MGS-GMRES

CC Paige, M Rozlozník, Z Strakos - SIAM Journal on Matrix Analysis and …, 2006 - SIAM
The generalized minimum residual method (GMRES)[Y. Saad and M. Schultz, SIAM J. Sci.
Statist. Comput., 7 (1986), pp. 856-869] for solving linear systems Ax= b is implemented as a …

Krylov methods for nonsymmetric linear systems

G Meurant, JD Tebbens - Cham: Springer, 2020 - Springer
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 …

[图书][B] A Journey through the History of Numerical Linear Algebra

C Brezinski, G Meurant, M Redivo-Zaglia - 2022 - SIAM
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 …

How to make simpler GMRES and GCR more stable

P Jiránek, M Rozložník, MH Gutknecht - SIAM journal on matrix analysis and …, 2009 - SIAM
In this paper we analyze the numerical behavior of several minimum residual methods
which are mathematically equivalent to the GMRES method. Two main approaches are …

Residual and backward error bounds in minimum residual Krylov subspace methods

CC Paige, Z Strakos - SIAM Journal on Scientific Computing, 2002 - SIAM
Minimum residual norm iterative methods for solving linear systems Ax= b can be viewed as,
and are often implemented as, sequences of least squares problems involving Krylov …

The role eigenvalues play in forming GMRES residual norms with non-normal matrices

G Meurant, J Duintjer Tebbens - Numerical Algorithms, 2015 - Springer
In this paper we give explicit expressions for the norms of the residual vectors generated by
the GMRES algorithm applied to a non-normal matrix. They involve the right-hand side of the …