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GMBACK

swMATH ID: 2139
Software Authors: Kasenally, Ebrahim M.
Description: GMBACK: A generalised minimum backward error algorithm for nonsymmetric linear systems A drawback of employing the residual error norm as a stopping condition in an iterative process is that the error must be small if the approximation is accurate. However, the converse need not be true. The main aims of this paper are to consider an alternative criterion for judging whether a given approximation is acceptable and to present an algorithm which computes an approximate solution to the linear system \(Ax = b\) such that the normwise backward error meets some optimality condition.
Homepage: http://epubs.siam.org/doi/abs/10.1137/0916042
Keywords: nonsymmetric linear systems; residual error norm; stopping condition; iterative process; algorithm; normwise backward error
Related Software: CGS; VanHuffel; LSQR; KELLEY; CRAIG; MINRES; LSMR; SparseMatrix; na1; JDQZ; GpBiCg; Eigtool; UTV; BiCGstab; JDQR; eigs; DQGMRES; Regularization tools; QMRPACK; LSODA
Cited in: 13 Documents

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
GMBACK: A generalised minimum backward error algorithm for nonsymmetric linear systems. Zbl 0823.65029
Kasenally, Ebrahim M.
1995
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Cited by 16 Authors

3 Cătinaş, Emil
2 Kasenally, Ebrahim M.
2 Simoncini, Valeria
2 Yang, Zhanshan
1 Alléon, Guillaume
1 Benzi, Michele
1 Giraud, Luc
1 Hallman, Eric
1 Liu, Xiaoming
1 Liu, Xilan
1 Liu, Yulu
1 Lu, Zhiming
1 Meister, Andreas
1 Szyld, Daniel B.
1 van Rienen, Ursula
1 Zheng, Bing
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Cited in 13 Serials

1 Journal of Computational Physics
1 Mathematics of Computation
1 Applied Mathematics and Computation
1 Journal of Optimization Theory and Applications
1 SIAM Journal on Numerical Analysis
1 Applied Mathematics and Mechanics. (English Edition)
1 SIAM Journal on Matrix Analysis and Applications
1 Numerical Algorithms
1 Revue d’Analyse Numérique et de Théorie de l’Approximation
1 SIAM Journal on Scientific Computing
1 Numerical Linear Algebra with Applications
1 JP Journal of Algebra, Number Theory and Applications
1 Lecture Notes in Computational Science and Engineering

Cited in 5 Fields

13 Numerical analysis (65-XX)
3 Linear and multilinear algebra; matrix theory (15-XX)
2 Fluid mechanics (76-XX)
2 Optics, electromagnetic theory (78-XX)
1 Geophysics (86-XX)

Citations by Year