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Computing extreme eigenvalues of large sparse symmetric problems. (English) Zbl 0819.65046

Dimov, I. T. (ed.) et al., Proceedings of the third international conference on advances in numerical methods and applications \(O(h^ 3)\), Sofia, Bulgaria, 21-26 August, 1994. Singapore: World Scientific. 40-46 (1994).
The authors discuss the application of new variants of the preconditioned power method for finding the lowest eigenvalue and corresponding eigenvector of a symmetric positive definite matrix. They briefly report theoretical results on global convergence of the considered algorithms. Numerical experiments with various preconditioners based on incomplete Cholesky factorization indicate that the algorithms presented are efficient.
For the entire collection see [Zbl 0801.00040].

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F35 Numerical computation of matrix norms, conditioning, scaling
65F50 Computational methods for sparse matrices
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