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 …
scientific computing. It appears in many areas like physics, engineering, chemistry, biology …
Convergence properties of block GMRES and matrix polynomials
This paper studies convergence properties of the block gmres algorithm when applied to
nonsymmetric systems with multiple right-hand sides. A convergence theory is developed …
nonsymmetric systems with multiple right-hand sides. A convergence theory is developed …
Restarted GMRES for shifted linear systems
A Frommer, U Glässner - SIAM Journal on Scientific Computing, 1998 - SIAM
Shifted matrices, which differ by a multiple of the identity only, generate the same Krylov
subspaces with respect to any fixed vector. This fact has been exploited in Lanczos-based …
subspaces with respect to any fixed vector. This fact has been exploited in Lanczos-based …
2D and 3D frequency-domain elastic wave modeling in complex media with a parallel iterative solver
Full-waveform inversion and reverse time migration rely on an efficient forward-modeling
approach. Current 3D large-scale frequency-domain implementations of these techniques …
approach. Current 3D large-scale frequency-domain implementations of these techniques …
[BOOK][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 …
[1] A. Abdelfattah, H. Anzt, A. Bouteiller, A. Danalis, JJ Dongarra, M. Gates, A. Haidar, J. Kurzak …
Deflated GMRES for systems with multiple shifts and multiple right-hand sides
We consider solution of multiply shifted systems of nonsymmetric linear equations, possibly
also with multiple right-hand sides. First, for a single right-hand side, the matrix is shifted by …
also with multiple right-hand sides. First, for a single right-hand side, the matrix is shifted by …
Flexible variants of block restarted GMRES methods with application to geophysics
In a wide number of applications in computational science and engineering the solution of
large linear systems of equations with several right-hand sides given at once is required …
large linear systems of equations with several right-hand sides given at once is required …
Block Modified Gram--Schmidt Algorithms and Their Analysis
JL Barlow - SIAM Journal on Matrix Analysis and Applications, 2019 - SIAM
New block modified Gram--Schmidt (BMGS) methods for the QR factorization of a full column
rank matrix X∈R^m*n, m≧n, are considered. Such methods factor X into Q∈R^m*n and an …
rank matrix X∈R^m*n, m≧n, are considered. Such methods factor X into Q∈R^m*n and an …
Block GMRES method with inexact breakdowns and deflated restarting
We consider the solution of large linear systems with multiple right-hand sides using a block
GMRES approach. We introduce a new algorithm that effectively handles the situation of …
GMRES approach. We introduce a new algorithm that effectively handles the situation of …
An Efficient and Accurate Penalty-projection Eddy Viscosity Algorithm for Stochastic Magnetohydrodynamic Flow Problems
We propose, analyze, and test a penalty projection-based robust efficient and accurate
algorithm for the Uncertainty Quantification (UQ) of the time-dependent …
algorithm for the Uncertainty Quantification (UQ) of the time-dependent …