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Abstract: Arnoldi methods can be more effective than subspace iteration methods for computing the dominant eigenvalues of a large sparse real unsymmetric matrix. A code, EB12, for the sparse unsymmetric eigenvalue problem based on a subspace iteration algorithm, optionally combined with Chebychev acceleration, has recently been described by Duff and Scott (1993) and is included in the Harwell Subroutine Library (Anon 1993). In this paper we consider variants of the method of Arnoldi and discuss the... (Update)
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.... based on a subspace iteration algorithm, optionally combined with Chebychev acceleration, has recently been described by Duff and Scott (1993) and is included in the Harwell Subroutine Library (Anon 1993) In this paper we consider variants of the method of Arnoldi and...
.... in the sparse symmetric eigenvalue problem, all algorithms known to us (see [BW 73, C 78, CD 74, DR 75, L 77, P 71, R 74, R 79, S 93, Sc 93, SLN 75, SBP 73, U 75] which compute the eigenvalues and eigenvectors of a sparse rational matrix by orthogonal factorizations z or...
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16: The Principle of Minimized Iteration in the Solution of Matrix Eigenvalue Proble.. (context) - Arnoldi - 1951
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BibTeX entry: (Update)
J. A. Scott. An Arnoldi code for computing selected eigenvalues of sparse real unsymmetric matrices. ACM Transactions on Mathematical Software, 21:432--475, 1995. http://citeseer.ist.psu.edu/scott95arnoldi.html More
@article{ scott95arnoldi,
author = "Jennifer A. Scott",
title = "An {Arnoldi} Code for Computing Selected Eigenvalues of Sparse, Real, Unsymmetric Matrices",
journal = "ACM Transactions on Mathematical Software",
volume = "21",
number = "4",
pages = "432--475",
year = "1995",
url = "citeseer.ist.psu.edu/scott95arnoldi.html" }
Citations (may not include all citations):245 An extended set of Fortran Basic Linear Algebra Subprograms - Dongarra, Du et al. - 1988
167 The principle of minimized iteration in the solution of matr.. (context) - Arnoldi - 1959
98 A set of Level 3 Basic Linear Algebra Subprograms (context) - Dongarra, Du et al. - 1990
92 Distribution of mathematical software via electronic mail (context) - Dongarra, Grosse - 1987
88 User's guide for the Harwell-Boeing sparse matrix collection (context) - Duff, Grimes et al. - 1992
66 Reorthogonalization and stable algorithms for updating the G.. (context) - Daniel, Gragg et al. - 1976
63 Variations on Arnoldi's method for computing eigenelements o.. (context) - Saad - 1980
39 Chebyshev acceleration techniques for solving nonsymmetric e.. (context) - Saad - 1984
28 ARPACK: An implementation of the Implicitly Re-started Arnol.. (context) - Lehoucq, Sorensen et al. - 1994
26 SRRIT -- A FORTRAN subroutine to calculate the dominant inva.. - Stewart - 1978
24 Complex shift and invert strategies for real matrices (context) - Parlett, Saad - 1985
24 An Arnoldi code for computing selected eigenvalues of sparse.. - Scott - 1993
21 a Fortran code for direct solution of sparse unsymmetric lin.. (context) - Duff, Reid - 1993
18 Qualitative computing: elements of a theory for finite-preci.. (context) - Chatelin, Fraysse - 1993
13 The Arnoldi-Tchebycheff algorithm for solving large nonsymme.. (context) - Braconnier - 1993
12 Tchebychev acceleration technique for large scale nonsymmetr.. (context) - Ho - 1990
12 Large-scale complex eigenvalue problems (context) - Kerner - 1989
11 Computing selected eigenvalues of large sparse unsymmetric m.. (context) - Duff, Scott - 1993
10 The Tchebyshev iteration for nonsymmetric linear systems (context) - Manteuffel - 1977
9 An iterative method for solving nonsymmetric linear systems .. (context) - Manteuffel - 1975
9 Arnoldi-Tchebychev procedure for large scale nonsymmetric ma.. (context) - Ho, Chatelin et al. - 1990
9 A collection of test matrices for the large scale nonsymmetr.. (context) - Bai - 1993
7 A relative backward perturbation theorem for the eigenvalue .. (context) - Deif - 1989
7 Numerical solution of large nonsymmetric eigenvalue problems - Saad - 1989
5 The numerical detection of Hopf bifurcation in large systems.. (context) - Garratt - 1991
4 Two methods for the numerical detection of Hopf bifurcations (context) - Garratt, Moore et al. - 1991
4 Eigenvalues of large highly nonnormal matrices (context) - Godet-Thobie - 1992
3 Eigenvectors of real and complex matrices by LR and QR facto.. (context) - Peters, Wilkinson - 1970
2 the solution of large sparse unsymmetric eigenvalue problems (context) - Sadkane
2 Private communication (context) - Garratt - 1990
1 A block Arnoldi-Chebychev method for computing the leading e.. (context) - Sadkane
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