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QMRPACK

swMATH ID: 754
Software Authors: Freund, Roland W.; Nachtigal, Noël M.
Description: QMRPACK: A package of QMR algorithms. The quasi-minimal residual (QMR) algorithm is a Krylov-subspace method for the iterative solution of large non-Hermitian linear systems. QMR is based on the look-ahead Lanczos algorithm that, by itself, can also be used to obtain approximate eigenvalues of large non-Hermitian matrices. QMRPACK is a software package with Fortran 77 implementations of the QMR algorithm and variants thereof, and of the three-term and coupled two-term look-ahead Lanczos algorithms. In this article, we discuss some of the features of the algorithms in the package, with emphasis on the issues related to using the codes. We describe in some detail two routines from the package, one for the solution of linear systems and the other for the computation of eigenvalue approximations. We present some numerical examples from applications where QMRPACK was used.
Homepage: http://www.cs.ucdavis.edu/~bai/ET/lanczos_methods/overview_QMRPACK.html
Keywords: quasi-minimal residual algorithm; Krylov-subspace method; large non-Hermitian linear systems; look-ahead Lanczos algorithm; software package; eigenvalue; numerical examples
Related Software: JDQZ; JDQR; ARPACK; LAPACK; HOPDM; BiCGstab; PETSc; PARDISO; eigs; CUTEst; SRRIT; ScaLAPACK; Matlab; Eigtool; CGS; LSQR; BLAS; ILUT; mctoolbox; JADAMILU
Cited in: 80 Documents

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
QMRPACK: A package of QMR algorithms. Zbl 0884.65027
Freund, Roland W.; Nachtigal, Noël M.
1996
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Cited by 134 Authors

11 Simoncini, Valeria
5 Bergamaschi, Luca
4 Bai, Zhaojun
4 Benzi, Michele
4 Freund, Roland W.
4 Gondzio, Jacek
4 Heinkenschloss, Matthias
4 Zilli, Giovanni
3 Bellavia, Stefania
3 Bollhöfer, Matthias
3 De Simone, Valentina
3 di Serafino, Daniela
3 Golub, Gene Howard
3 Morini, Benedetta
2 Chen, Xi
2 Edlund, Åke
2 Gu, Xian-Ming
2 Gutknecht, Martin H.
2 Herty, Michael Matthias
2 Huang, Ting-Zhu
2 Liu, Yijun
2 Malhotra, Manish
2 Nachtigal, Noël M.
2 Notay, Yvan
2 Perotti, Federico
2 Peskin, Uri
2 Pestana, Jennifer
2 Phoon, Kok-Kwang
2 Römer, Rudolf A.
2 Schenk, Olaf
2 Szyld, Daniel B.
2 Toh, Kim Chuan
2 Van der Vorst, Henk Albertus
2 Venturin, Manolo
2 Wathen, Andrew John
1 Adlerborn, Björn
1 Agoujil, Said
1 Arbenz, Peter
1 Arioli, Mario
1 Ashby, Thomas J.
1 Bar-On, Ilan
1 Barbella, G.
1 Bartlett, Roscoe A.
1 Benoît, René
1 Bentbib, Abdeslem Hafid
1 Broyden, Charles George
1 Cao, Zhihao
1 Chen, Shaohai
1 Chen, Xiaolin
1 Clemens, Markus
1 Dackland, Krister
1 D’Apuzzo, Marco
1 Demmel, James Weldon
1 Desgagné, M.
1 Dongarra, Jack J.
1 Dougalis, Vassilios A.
1 Duintjer Tebbens, Jurjen
1 Elsner, Ulrich
1 Facchinei, Francisco
1 Feriani, Anna
1 Ferris, Michael C.
1 Ferronato, Massimiliano
1 Fischer, Andreas
1 Fujiwara, Takeo
1 Gambolati, Giuseppe
1 Geus, Roman
1 Grote, Marcus J.
1 Gupta, Anshul
1 Güttel, Stefan
1 Haber, Eldad
1 Heroux, Michael A.
1 Hochstenbach, Michiel E.
1 Hon, Sean Y.
1 Hoshi, Takeo
1 Janssen, Curtis L.
1 Kågström, Bo
1 Kampanis, Nikolaos A.
1 Kanber, Ahmed
1 Kanzow, Christian
1 Karim, Samah
1 Kennedy, Anthony D.
1 Klawonn, Axel
1 Lehoucq, Richard B.
1 Lenhardt, Ingrid
1 Li, Congcong
1 Li, Liang
1 Liesen, Jörg
1 Lin, Xuelei
1 Malevsky, Andrei V.
1 Meerbergen, Karl
1 Mehrmann, Volker
1 Meurant, Gérard A.
1 Milde, Frank
1 Morel, Jim E.
1 Munson, Todd S.
1 Natarajan, Ramesh
1 Nguyen, Hoang Q.
1 Nielsen, Ida M. B.
1 O’Boyle, Michael F. P.
1 Pavarino, Luca Franco
...and 34 more Authors
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Cited in 28 Serials

8 SIAM Journal on Matrix Analysis and Applications
8 SIAM Journal on Scientific Computing
7 Applied Numerical Mathematics
6 Computer Methods in Applied Mechanics and Engineering
6 Numerical Linear Algebra with Applications
5 Computational Optimization and Applications
4 Journal of Computational Physics
3 Computer Physics Communications
2 BIT
2 Journal of Computational and Applied Mathematics
2 Numerische Mathematik
2 Parallel Computing
2 Acta Numerica
1 ACM Transactions on Mathematical Software
1 International Journal for Numerical Methods in Engineering
1 Journal of Scientific Computing
1 Numerical Algorithms
1 Linear Algebra and its Applications
1 SIAM Review
1 SIAM Journal on Optimization
1 INFORMS Journal on Computing
1 CMES. Computer Modeling in Engineering & Sciences
1 IEEE Transactions on Antennas and Propagation
1 Journal of Computational Acoustics
1 Studies in Computational Mathematics
1 Software - Environments - Tools
1 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche
1 Advances in Applied Mathematics and Mechanics
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Cited in 18 Fields

69 Numerical analysis (65-XX)
11 Operations research, mathematical programming (90-XX)
9 Optics, electromagnetic theory (78-XX)
8 Partial differential equations (35-XX)
7 Linear and multilinear algebra; matrix theory (15-XX)
7 Mechanics of deformable solids (74-XX)
7 Fluid mechanics (76-XX)
5 Calculus of variations and optimal control; optimization (49-XX)
2 Dynamical systems and ergodic theory (37-XX)
2 Computer science (68-XX)
2 Statistical mechanics, structure of matter (82-XX)
2 Geophysics (86-XX)
1 General and overarching topics; collections (00-XX)
1 History and biography (01-XX)
1 Mechanics of particles and systems (70-XX)
1 Quantum theory (81-XX)
1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
1 Information and communication theory, circuits (94-XX)

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