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CGS

swMATH ID: 8225
Software Authors: Sonneveld, Peter
Description: CGS, a fast Lanczos-type solver for nonsymmetric linear systems. The presented method is a combination of the CGS algorithm (a “squared” conjugate gradient method) with a preconditioning called ILLU (an incomplete line-LU-factorization). The conclusion of the author is that this combination is a competitive solver for nonsymmetric linear systems, at least for problems that are not too large, and when high accuracy is required. Numerical experiments show that the average work for solving convection-diffusion equations in two dimensions is roughly O(N 3/2 ).
Homepage: http://dl.acm.org/citation.cfm?id=64888
Keywords: squared conjugate gradient method; preconditioning; incomplete line-LU- factorization; nonsymmetric linear systems; convection-diffusion equations
Related Software: BiCGstab; GpBiCg; na1; SparseMatrix; symrcm; Harwell-Boeing sparse matrix collection; LSQR; SPARSKIT; na5; ILUT; Bi-CG; ITSOL; NSPCG; Wesseling; BLAS; CORS; BiCOR; LAPACK; Matlab; MatrixMarket
Cited in: 329 Publications

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
CGS, a fast Lanczos-type solver for nonsymmetric linear systems. Zbl 0666.65029
Sonneveld, Peter
1989
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Cited by 449 Authors

15 Van der Vorst, Henk Albertus
11 Brezinski, Claude
11 Sleijpen, Gerard L. G.
9 Huang, Ting-Zhu
7 Wille, Sven Øivind
6 Carpentieri, Bruno
6 Chan, Tony Fan-Cheong
6 Ching, Wai-Ki
6 Redivo-Zaglia, Michela
6 Sadok, Hassane
5 Bai, Zhengjian
5 Jing, Yanfei
5 Sugihara, Masaaki
5 Van Gijzen, Martin Bastiaan
5 Zhang, Shao-Liang
4 Abe, Kuniyoshi
4 Forsyth, Peter A.
4 Gutknecht, Martin H.
4 Shapira, Yair
4 Sheu, Tony Wen-Hann
4 Sonneveld, Peter
4 Zhang, Jun
3 Aihara, Kensuke
3 Cao, Zhihao
3 Chan, Raymond Hon-Fu
3 Chien, Cheng-Sheng
3 de Sturler, Eric
3 Dehghan Takht Fooladi, Mehdi
3 Dongarra, Jack J.
3 Eijkhout, Victor L.
3 Ferronato, Massimiliano
3 Freund, Roland W.
3 Gravvanis, George A.
3 Gu, Xian-Ming
3 Hajarian, Masoud
3 Juncu, Gheorghe
3 Keyes, David Elliot
3 Li, Liang
3 Loula, Abimael Fernando Dourado
3 Maubach, Joseph M. L.
3 Mayo, Anita A.
3 Pina, Heitor L. G.
3 Popa, Constantin
3 Rabier, Patrick J.
3 Saad, Yousef
3 Sogabe, Tomohiro
3 Tong, Charles H.
3 Valente, F. P.
3 Vuik, Cornelis
3 Yun, Jae Heon
3 Zhang, Liwei
2 Ahuja, Kapil
2 Bank, Randolph E.
2 Barrett, Richard K.
2 Belliard, Michel
2 Berry, Michael W.
2 Chang, Tsai-Shou
2 Chen, Jinhai
2 Dai, Hua
2 de Araújo, Francisco Célio
2 Doi, Shun
2 Duan, Yong
2 Ellabib, Abdellatif
2 Erlangga, Yogi A.
2 Evans, David John
2 Fokkema, Diederik R.
2 Fortin, Michel
2 Fujino, Seiji
2 Gambolati, Giuseppe
2 Georgiev, Krassimir
2 Greenbaum, Anne
2 Gu, Tongxiang
2 Habashi, Wagdi G.
2 Heinreichsberger, O.
2 Holmgren, Sverker
2 Ishiwata, Emiko
2 Jbilou, Khalide
2 Jiang, Hong
2 Langtangen, Hans Petter
2 Layton, William J.
2 Li, Lidan
2 Lin, Wen-Wei
2 Liu, Xingping
2 Lukšan, Ladislav
2 Ma, Changfeng
2 Meister, Andreas
2 Meurant, Gérard A.
2 Molavi-Arabshahi, Seyedeh Mahboubeh
2 Nachaoui, Abdeljalil
2 Nachtigal, Noël M.
2 Navon, Ionel Michael
2 Otto, Kurt
2 Peskin, Charles S.
2 Pini, Giorgio
2 Pommerell, Claude
2 Ramière, Isabelle
2 Robichaud, Michel P.
2 Romine, Charles H.
2 Selberherr, Siegfried
2 Staff, Ørnulf
...and 349 more Authors
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Cited in 63 Serials

38 Journal of Computational and Applied Mathematics
24 Applied Numerical Mathematics
23 Applied Mathematics and Computation
21 SIAM Journal on Scientific Computing
16 Computers & Mathematics with Applications
16 Numerical Algorithms
15 Journal of Computational Physics
13 Computer Methods in Applied Mechanics and Engineering
11 International Journal for Numerical Methods in Fluids
11 SIAM Journal on Matrix Analysis and Applications
11 Linear Algebra and its Applications
8 Engineering Analysis with Boundary Elements
7 BIT
7 Numerische Mathematik
7 Numerical Linear Algebra with Applications
5 SIAM Journal on Scientific and Statistical Computing
4 Computer Physics Communications
4 International Journal for Numerical Methods in Engineering
4 Applied Mathematics Letters
4 International Journal of Computer Mathematics
3 Computers and Fluids
3 Mathematics and Computers in Simulation
3 Parallel Computing
3 Computational Mechanics
3 Archives of Computational Methods in Engineering
2 International Journal of Heat and Mass Transfer
2 International Journal for Numerical and Analytical Methods in Geomechanics
2 Inverse Problems
2 Journal of the Franklin Institute
2 Mathematics of Computation
2 Computing
2 Journal of Optimization Theory and Applications
2 Numerical Methods for Partial Differential Equations
2 Applied Mathematical Modelling
2 Computational and Applied Mathematics
2 Advances in Computational Mathematics
1 Journal of Engineering Mathematics
1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)
1 Numerical Functional Analysis and Optimization
1 Applied Mathematics and Mechanics. (English Edition)
1 Acta Applicandae Mathematicae
1 RAIRO. Modélisation Mathématique et Analyse Numérique
1 Communications in Applied Numerical Methods
1 Computers & Operations Research
1 Journal of Economic Dynamics & Control
1 Journal of Scientific Computing
1 Japan Journal of Industrial and Applied Mathematics
1 International Journal of High Speed Computing
1 The Journal of Supercomputing
1 Journal of Non-Newtonian Fluid Mechanics
1 SIAM Review
1 Computational Optimization and Applications
1 Communications in Numerical Methods in Engineering
1 International Journal of Numerical Methods for Heat & Fluid Flow
1 Computational Geosciences
1 IEEE Transactions on Image Processing
1 Central European Journal of Mathematics
1 Acta Numerica
1 Journal of Industrial and Management Optimization
1 Lecture Notes in Computational Science and Engineering
1 ISRN Applied Mathematics
1 International Journal of Applied and Computational Mathematics
1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys

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