Pdf J.h.wilkinson C.reinsch Handbook For Automatic Computation Pdf

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Chebyshev acceleration techniques for solving nonsymmetric eigenvalue problems

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Author:Youcef Saad
Journal:Math. Comp. 42 (1984), 567-588
MSC:Primary 65F15; Secondary 65F50
DOI:https://doi.org/10.1090/S0025-5718-1984-0736453-8
MathSciNet review:736453
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Abstract: The present paper deals with the problem of computing a few of the eigenvalues with largest (or smallest) real parts, of a large sparse nonsymmetric matrix. We present a general acceleration technique based on Chebyshev polynomials and discuss its practical application to Arnoldi's method and the subspace iteration method. The resulting algorithms are compared with the classical ones in a few experiments which exhibit a sharp superiority of the Arnoldi-Chebyshev approach.

Pdf J.h.wilkinson C.reinsch Handbook For Automatic Computation Pdf Software

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Full-text PDF Free Access. Abstract References. Handbook for automatic computation. II, Springer-Verlag, New York-Heidelberg, 1971. Linear algebra; Compiled by J. Wilkinson and C. Reinsch; Die Grundlehren der Mathematischen Wissenschaften, Band 186. Wilkinson Publisher: Springer ISBN: 146 Size: 24.48 MB Format: PDF, Docs Category: Computers Languages: en Pages: 441 View: 5839 Book Description: The development of the internationally standardized language ALGOL has made it possible to prepare procedures which can be used without modification whenever a computer with an ALGOL translator is available. Full-text PDF Free Access. Handbook for automatic computation. II, Springer-Verlag, New York-Heidelberg, 1971. Linear algebra; Compiled by J. Linear algebra; Compiled by J. Wilkinson and C. Reinsch; Die Grundlehren der Mathematischen Wissenschaften, Band 186. MR 0461856 43 H. Wrigley, Accelerating the Jacobi method for solving simultaneous equations by Chebyshev extrapolation when the eigenvalues of the iteration matrix are complex, Comput. Advancing research. Creating connections. ISSN 1088-6842(online) ISSN 0025-5718(print).

Quart Appl. Math., v. 9, 1951, pp. 17-29. MR 0042792 (13:163e)
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F. L. Bauer, 'Das Verfahren der Treppeniteration und Verwandte Verfahren zur Losung Algebraischer Eigenwertprobleme,' Z. Angew. Math. Phys., v. 8, 1957, pp. 214-235. MR 0088049 (19:461b)
[3]
A. Clayton, Further Results on Polynomials Having Least Maximum Modulus Over an Ellipse in the Complex Plane, Technical Report AEEW-7348, UKAEA, 1963.
[4]
M Clint & A. Jennings, 'The evaluation of eigenvalues and eigenvectors of real symmetric matrices by simultaneous iteration method,' J. Inst. Math. Appl., v. 8, 1971, pp. 111-121. MR 0297116 (45:6174)
[5]
F. D'Almeida, Numerical Study of Dynamic Stability of Macroeconomical Models-Software for MODULECO, Dissertation, Technical Report INPG-University of Grenoble, 1980. (French)
[6]
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[7]
H. C. Elman, Iterative Methods for Large Sparse Nonsymmetric Systems of Linear Equations, Ph.D. thesis, Technical Report 229, Yale University, 1982.
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H. C. Elman, Y. Saad & P.Saylor, A New Hybrid Chebyshev Algorithm for Solving Nonsymmetric Systems of Linear Equations. Technical Report, Yale University, 1984.
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Y. Saad, 'Projection methods for solving Large sparse eigenvalue problems,' in Matrix Pencils, Proceedings (Pitea Havsbad, B. Kagstrom and A. Ruhe, eds.), Lecture Notes in Math., vol. 973, Springer-Verlag, Berlin, 1982, pp. 121-144.
[31]
Y. Saad, Least Squares Polynomials in the Complex Plane with Applications to Solving Sparse Nonsymmetric Matrix Problems, Technical Report RR-276, Dept. of Computer Science, Yale University, 1983.
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Y. Saad, 'Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices,' Linear Algebra Appl., v. 34, 1980, pp. 269-295. MR 591435 (81m:65055)
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D. C. Smolarski & P. E. Saylor, Optimum Parameters for the Solution of Linear Equations by Richardson Iteration, 1982. Unpublished Manuscript.
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G. W. Stewart, 'Simultaneous iteration for computing invariant subspaces of non-Hermitian matrices,' Numer. Math., v. 25, 1976, pp. 123-136. MR 0400677 (53:4508)
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G. W. Stewart, SRRIT-A FORTRAN Subroutine to Calculate the Dominant Invariant Subspaces of a Real Matrix, Technical Report TR-514, Univ. of Maryland, 1978.
[40]
D. Taylor, Analysis of the Look-Ahead Lanczos Algorithm, Ph.D. thesis, Technical Report, Univ. of California, Berkeley, 1983.
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DOI:https://doi.org/10.1090/S0025-5718-1984-0736453-8
Article copyright:© Copyright 1984American Mathematical Society