Wu, Kesheng; Simon, Horst Thick-restart Lanczos method for large symmetric eigenvalue problems. (English) Zbl 0969.65030 SIAM J. Matrix Anal. Appl. 22, No. 2, 602-616 (2000). An explicitly restarted symmetric Lanczos algorithm described in this paper belongs to a class which is (theoretically) equivalent to its implicitly restarted alternative. Its main merit is that it is simpler to use. The proposed variant minimizes the cost of the restart by retaining many “older” Ritz vectors, and optimizes their selection. A number of numerical experiments is presented. The loss of the orthogonality (which is well know to require a reorthogonalization) is dealt with by using an economical partial reorthogonalization scheme. Reviewer: Miloslav Znojil (Řež) Cited in 1 ReviewCited in 82 Documents MSC: 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 65F25 Orthogonalization in numerical linear algebra Keywords:Lanczos method; explicit restart; partial reorthogonalization; large symmetric eigenvalue problems; Ritz vectors; numerical experiments Software:TRLan; JDQR; ARPACK; Harwell-Boeing sparse matrix collection; AztecOO; JDQZ; Aztec; PETSc; BLZPACK; BlockSolve95 PDFBibTeX XMLCite \textit{K. Wu} and \textit{H. Simon}, SIAM J. Matrix Anal. Appl. 22, No. 2, 602--616 (2000; Zbl 0969.65030) Full Text: DOI