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 0666.65029Sonneveld, Peter 1989 all top 5 Cited by 451 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 351 more Authors all top 5 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 all top 5 Cited in 28 Fields 277 Numerical analysis (65-XX) 67 Partial differential equations (35-XX) 59 Fluid mechanics (76-XX) 16 Linear and multilinear algebra; matrix theory (15-XX) 15 Mechanics of deformable solids (74-XX) 12 Optics, electromagnetic theory (78-XX) 10 Computer science (68-XX) 10 Operations research, mathematical programming (90-XX) 6 Ordinary differential equations (34-XX) 6 Probability theory and stochastic processes (60-XX) 6 Classical thermodynamics, heat transfer (80-XX) 5 Systems theory; control (93-XX) 5 Information and communication theory, circuits (94-XX) 3 Potential theory (31-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 History and biography (01-XX) 2 Functions of a complex variable (30-XX) 2 Operator theory (47-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Geophysics (86-XX) 2 Biology and other natural sciences (92-XX) 1 Algebraic geometry (14-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Mechanics of particles and systems (70-XX) 1 Quantum theory (81-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year