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Solving Sparse Symmetric Generalized Eigenvalue Problems without Factorization

Journal Article · · SIAM Journal on Numerical Analysis
DOI:https://doi.org/10.1137/0718008· OSTI ID:5879482

An iterative technique is discussed for finding the algebraically smallest (or largest) eigenvalue of the generalized eigenvalue problem A - lambdaM, where A and M are real and symmetric, and M is positive definite. It is assumed that A and M are such that it is undesirable to factor the matrix A - sigmaM for any value of sigma. It is proved that the algorithm is globally convergent and that convergence is asymptotically quadratic. Finally, the modifications required in the algorithm to make it computationally feasible are discussed. 7 tables.

Research Organization:
Oak Ridge National Lab., TN (USA)
Sponsoring Organization:
USDOE
Grant/Contract Number:
W-7405-ENG-26
OSTI ID:
5879482
Alternate ID(s):
OSTI ID: 6151892
Report Number(s):
ORNL/CSD-49
Journal Information:
SIAM Journal on Numerical Analysis, Journal Name: SIAM Journal on Numerical Analysis Journal Issue: 1 Vol. 18; ISSN 1095-7170; ISSN 0036-1429
Publisher:
Society for Industrial and Applied Mathematics (SIAM)Copyright Statement
Country of Publication:
United States
Language:
English

References (4)

A new iterative method for solution of a large-scale general eigenvalue problem journal August 1978
A new look at the Lanczos algorithm for solving symmetric systems of linear equations journal February 1980
The Lanczos algorithm with selective orthogonalization journal January 1979
An energy principle for hydromagnetic stability problems
  • Bernstein, I. B.; Frieman, E. A.; Kruskal, Martin David
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 244, Issue 1236, p. 17-40 https://doi.org/10.1098/rspa.1958.0023
journal February 1958

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Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
CALCULATION METHODS
EIGENVALUES
ITERATIVE METHODS
MATHEMATICAL LOGIC
MATRICES
SERIES EXPANSION