Brand, Clemens W.; Petrova, Svetozara 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]. Reviewer: Z.Dostál (Ostrava) MSC: 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 65F35 Numerical computation of matrix norms, conditioning, scaling 65F50 Computational methods for sparse matrices Keywords:large sparse symmetric problems; numerical experiments; preconditioned power method; lowest eigenvalue; eigenvector; symmetric positive definite matrix; convergence; incomplete Cholesky factorization PDFBibTeX XMLCite \textit{C. W. Brand} and \textit{S. Petrova}, in: 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; Zbl 0819.65046)