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IRAM

swMATH ID: 8795
Software Authors: Sorensen, Danny C.
Description: Implicit application of polynomial filters in a k-step Arnoldi method. 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://epubs.siam.org/doi/abs/10.1137/0613025
Keywords: Arnoldi method; eigenvalues; eigenvectors; Lanczos method; implicitly shifted \(QR\)-iteration; polynomial filter; explicit restart methods; parallel and vector computers
Related Software: eigs; ARPACK; JDQZ; JDQR; TRLan; Harwell-Boeing sparse matrix collection; Matlab; lobpcg.m; LAPACK; PROPACK; SLEPc; SparseMatrix; MatrixMarket; Eigtool; PRIMME; Algorithm 432; mctoolbox; EIGIFP; a-TRLan; FEAST
Cited in: 205 Publications
all top 5

Cited by 307 Authors

10 Jia, Zhongxiao
9 Wu, Gang
8 Meerbergen, Karl
7 Morgan, Ronald B.
6 Baglama, James
6 Lin, Wen-Wei
6 Reichel, Lothar
6 Sorensen, Danny C.
5 Faßbender, Heike
5 Zhou, Yunkai
4 Abdel-Aziz, Mohammedi R.
4 Benner, Peter
4 Calvetti, Daniela
4 Dax, Achiya
4 Miao, Cun-Qiang
4 Vandebril, Raf
3 Aishima, Kensuke
3 Bhuruth, Muddun
3 Camps, Daan
3 Dookhitram, Kumar
3 Embree, Mark
3 Gu, Chuanqing
3 Katsouleas, Georgios
3 Maroulas, John
3 Niu, Datian
3 Watkins, David S.
2 Antoulas, Athanasios C.
2 Bella, Tom
2 Boojhawon, Ravindra
2 Brandts, Jan H.
2 Bujanović, Zvonimir
2 Bultheel, Adhemar François
2 Canning, Andrew
2 Chen, Guizhi
2 Chen, Zhibing
2 Daube, Olivier
2 De Samblanx, Gorik
2 Gugercin, Serkan
2 Hansen, Per Christian
2 Hochstenbach, Michiel E.
2 Hou, Thomas Yizhao
2 Huang, Tsungming
2 Huang, Weiqiang
2 Kressner, Daniel
2 Le Quéré, Patrick
2 Li, Yiming
2 Lu, Linzhang
2 Mehrmann, Volker
2 Picucci, Jennifer
2 Plestenjak, Bor
2 Polizzi, Eric
2 Román, Jose E.
2 Rommes, Joost
2 Rostami, Minghao W.
2 Ruhe, Axel
2 Saad, Yousef
2 Sadkane, Miloud
2 Shieh, Shih-Feng
2 Simoncini, Valeria
2 Stoll, Martin
2 Van der Vorst, Henk Albertus
2 Van Dooren, Paul M.
2 Vömel, Christof
2 Wang, Lin-Wang
2 Yuan, Xuegang
1 Afanasiev, Konstantin
1 Ainsworth, G. O. jun.
1 Amodei, Luca
1 Andriano, C.
1 Apel, Thomas
1 Astudillo, Reinaldo
1 Bagheri, Shervin
1 Bai, Zhaojun
1 Ballard, Grey M.
1 Bekas, Constantine
1 Booten, Albert G. L.
1 Bosch, Jessica
1 Brogaard Riis, Nicolai André
1 Bucci, Michele Alessandro
1 Buchot, Jean-Marie
1 Bunse-Gerstner, Angelika
1 Caboussat, Alexandre
1 Calo, Victor Manuel
1 Campos, Carmen
1 Carden, Russell L.
1 Carson, Erin Claire
1 Chang, Shu-Ming
1 Chang, Wei-Jen
1 Cherubini, Stefania
1 Choi, Young-Geun
1 Chou, So-Hsiang
1 Cooke, S. J.
1 Cox, Steven J.
1 Cullum, Jane K.
1 da Silva, Ricardo Reis
1 D’Almeida, Filomena D.
1 Darnell, Dean
1 Dartora, C. A.
1 David, Roden J. A.
1 Demmel, James Weldon
...and 207 more Authors
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Cited in 50 Serials

30 Linear Algebra and its Applications
26 Journal of Computational and Applied Mathematics
12 Journal of Computational Physics
12 Applied Mathematics and Computation
12 BIT
12 Numerical Algorithms
10 SIAM Journal on Scientific Computing
8 Mathematical and Computer Modelling
8 Numerical Linear Algebra with Applications
7 Computer Methods in Applied Mechanics and Engineering
5 Applied Numerical Mathematics
5 SIAM Journal on Matrix Analysis and Applications
4 Computers & Mathematics with Applications
4 Mathematics of Computation
4 Numerische Mathematik
4 Journal of Scientific Computing
2 International Journal for Numerical Methods in Fluids
2 Journal of Fluid Mechanics
2 Systems & Control Letters
2 Japan Journal of Industrial and Applied Mathematics
2 Multiscale Modeling & Simulation
2 East Asian Journal on Applied Mathematics
1 Computers and Fluids
1 Physics Reports
1 Calcolo
1 Journal of Multivariate Analysis
1 Mathematics and Computers in Simulation
1 Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik
1 Computer Aided Geometric Design
1 Physica D
1 Computational Mechanics
1 Applied Mathematics Letters
1 Journal of Parallel and Distributed Computing
1 Applications of Mathematics
1 Mathematical Programming. Series A. Series B
1 Archive of Applied Mechanics
1 ETNA. Electronic Transactions on Numerical Analysis
1 ELA. The Electronic Journal of Linear Algebra
1 Mathematical Problems in Engineering
1 European Journal of Control
1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
1 Archives of Computational Methods in Engineering
1 SIAM Journal on Applied Dynamical Systems
1 Acta Numerica
1 GAMM-Mitteilungen
1 Communications in Computational Physics
1 Science China. Mathematics
1 Afrika Matematika
1 International Journal of Applied and Computational Mathematics
1 Results in Applied Mathematics

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