## eigs

 swMATH ID: 3702 Software Authors: MathWorks, Inc.; Sorensen, Danny C. Description: eigs: Largest eigenvalues and eigenvectors of matrix The author describes and analyses a new implementation of the Arnoldi method for computing a few eigenvalues and the corresponding eigenvectors of a large general square matrix (which reduces to the Lanczos method in the symmetric case). Using a truncated variant of the implicitly shifted QR-iteration, the author applies a polynomial filter to the Arnoldi (Lanczos) vector on each iteration. This approach generalizes explicit restart methods. Advantages of the method are discussed and some preliminary computational results using parallel and vector computers are given. Homepage: http://www.mathworks.com/help/matlab/ref/eigs.html Dependencies: Matlab Related Software: IRAM; ARPACK; JDQZ; JDQR; Eigtool; Matlab; Harwell-Boeing sparse matrix collection; TRLan; LAPACK; lobpcg.m; PROPACK; MatrixMarket; Seigtool; SparseMatrix; mctoolbox; BLAS; SRRIT; na26; Algorithm 432; SLEPc Cited in: 326 Publications

### Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
Implicit application of polynomial filters in a $$k$$-step Arnoldi method. Zbl 0763.65025
Sorensen, Danny C.
1992
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### Cited by 476 Authors

 13 Jia, Zhongxiao 12 Reichel, Lothar 12 Sorensen, Danny C. 11 Meerbergen, Karl 9 Wu, Gang 7 Baglama, James 7 Benner, Peter 7 Zhou, Yunkai 6 Abdel-Aziz, Mohammedi R. 6 Calvetti, Daniela 6 Faßbender, Heike 6 Morgan, Ronald B. 6 Najafi, H. Saberi 6 Saad, Yousef 5 Gattringer, Christof 5 Lin, Wen-Wei 5 Szularz, Marek 5 Weston, J. S. 4 Clint, Maurice 4 Hebermehl, Georg 4 Heinrich, Wolfgang 4 Niu, Datian 4 Sadkane, Miloud 4 Schlundt, Rainer 4 Stathopoulos, Andreas 4 Van der Vorst, Henk Albertus 4 Van Dooren, Paul M. 4 Vandebril, Raf 4 Watkins, David S. 4 Zscheile, Horst 3 Antoulas, Athanasios C. 3 Bai, Zhaojun 3 Camps, Daan 3 Eldén, Lars 3 Embree, Mark 3 Ghazvini, H. 3 Göckeler, Meinulf 3 Golub, Gene Howard 3 Grimme, Eric 3 Hip, Ivan 3 Hochstenbach, Michiel E. 3 Lang, Christian B. 3 Lehoucq, Richard B. 3 Mehrmann, Volker 3 Miao, Cun-Qiang 3 Rakow, Paul E. L. 3 Refahi, A. H. 3 Román, Jose E. 3 Ruhe, Axel 3 Schmid, Peter Joseph 3 Simoncini, Valeria 3 Spence, Alastair 3 Stoll, Martin 3 Trefethen, Lloyd Nicholas 2 Arbenz, Peter 2 Bella, Tom 2 Bhuruth, Muddun 2 Björck, Åke 2 Boojhawon, Ravindra 2 Brandts, Jan H. 2 Bujanović, Zvonimir 2 Bultheel, Adhemar François 2 Canning, Andrew 2 Chen, Guizhi 2 Daube, Olivier 2 Dax, Achiya 2 De Samblanx, Gorik 2 Dongarra, Jack J. 2 Dookhitram, Kumar 2 Drmač, Zlatko 2 Duintjer Tebbens, Jurjen 2 Emad, Nahid 2 Grote, Marcus J. 2 Gu, Chuanqing 2 Gugercin, Serkan 2 Hansen, Per Christian 2 Heuveline, Vincent 2 Higham, Nicholas J. 2 Hou, Thomas Yizhao 2 Huang, Tsungming 2 Huang, Weiqiang 2 Hübner, Friedrich-Karl 2 Katsouleas, Georgios 2 Kressner, Daniel 2 Le Quéré, Patrick 2 Li, Yiming 2 Lu, Linzhang 2 Maroulas, John 2 Nahum, Uri 2 Noschese, Silvia 2 Picucci, Jennifer 2 Plestenjak, Bor 2 Rostami, Minghao W. 2 Schäfer, Stefan 2 Shieh, Shih-Feng 2 Tischler, Thorsten 2 Tisseur, Françoise 2 Vömel, Christof 2 Wang, Lin-Wang 2 Wei, Yimin ...and 376 more Authors
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### Cited in 84 Serials

 29 Linear Algebra and its Applications 27 Journal of Computational and Applied Mathematics 24 SIAM Journal on Scientific Computing 21 Numerical Linear Algebra with Applications 20 SIAM Journal on Matrix Analysis and Applications 19 Applied Mathematics and Computation 15 Journal of Computational Physics 13 Numerical Algorithms 12 BIT 9 Mathematical and Computer Modelling 7 Journal of Fluid Mechanics 7 Applied Numerical Mathematics 6 Computer Methods in Applied Mechanics and Engineering 6 ETNA. Electronic Transactions on Numerical Analysis 5 Computers & Mathematics with Applications 4 Mathematics of Computation 4 Numerische Mathematik 3 International Journal for Numerical Methods in Fluids 3 Nuclear Physics. B 3 Theoretical and Computational Fluid Dynamics 3 Parallel Computing 3 Journal of Scientific Computing 2 Computers and Fluids 2 ACM Transactions on Mathematical Software 2 Mathematics and Computers in Simulation 2 COMPEL 2 Japan Journal of Industrial and Applied Mathematics 2 Mathematical Programming. Series A. Series B 2 Nuclear Physics. B. Proceedings Supplements 2 Multiscale Modeling & Simulation 2 East Asian Journal on Applied Mathematics 1 Computer Physics Communications 1 Computers and Structures 1 Inverse Problems 1 Nonlinearity 1 Physica A 1 Physics Letters. B 1 Physics Reports 1 International Journal for Numerical Methods in Engineering 1 Journal of Multivariate Analysis 1 Journal of Optimization Theory and Applications 1 Numerical Functional Analysis and Optimization 1 Systems & Control Letters 1 Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik 1 Computer Aided Geometric Design 1 Journal of Computational Mathematics 1 Physica D 1 Computational Mechanics 1 Asia-Pacific Journal of Operational Research 1 Applied Mathematics Letters 1 Journal of Parallel and Distributed Computing 1 Neural Networks 1 Signal Processing 1 Surveys on Mathematics for Industry 1 Applications of Mathematics 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 International Journal of Computer Mathematics 1 Archive of Applied Mechanics 1 SIAM Journal on Optimization 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Computational Optimization and Applications 1 Physics of Fluids 1 Computational and Applied Mathematics 1 ELA. The Electronic Journal of Linear Algebra 1 Parallel Algorithms and Applications 1 European Journal of Control 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Optimization Methods & Software 1 Taiwanese Journal of Mathematics 1 Mathematical Methods of Operations Research 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 International Journal of Numerical Modelling 1 International Journal of Applied Mathematics and Computer Science 1 Far East Journal of Mathematical Sciences 1 The ANZIAM Journal 1 Archives of Computational Methods in Engineering 1 GAMM-Mitteilungen 1 Software - Environments - Tools 1 Advances in Data Analysis and Classification. ADAC 1 Communications in Computational Physics 1 Science China. Mathematics 1 International Journal of Applied and Computational Mathematics 1 Lecture Notes in Electrical Engineering 1 Results in Applied Mathematics
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### Cited in 31 Fields

 260 Numerical analysis (65-XX) 52 Linear and multilinear algebra; matrix theory (15-XX) 31 Fluid mechanics (76-XX) 23 Systems theory; control (93-XX) 20 Partial differential equations (35-XX) 14 Quantum theory (81-XX) 12 Optics, electromagnetic theory (78-XX) 12 Operations research, mathematical programming (90-XX) 11 Computer science (68-XX) 11 Statistical mechanics, structure of matter (82-XX) 9 Mechanics of deformable solids (74-XX) 6 Ordinary differential equations (34-XX) 5 Statistics (62-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Probability theory and stochastic processes (60-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Operator theory (47-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Geophysics (86-XX) 2 Information and communication theory, circuits (94-XX) 1 Combinatorics (05-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Differential geometry (53-XX) 1 Mechanics of particles and systems (70-XX) 1 Biology and other natural sciences (92-XX)