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 0763.65025Sorensen, Danny C. 1992 all top 5 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 all top 5 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. 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Mathematics 1 International Journal of Applied and Computational Mathematics 1 Lecture Notes in Electrical Engineering 1 Results in Applied Mathematics all top 5 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) Citations by Year