Zhang, T.; Law, K. H.; Golub, G. H. On the homotopy method for perturbed symmetric generalized eigenvalue problems. (English) Zbl 0917.65035 SIAM J. Sci. Comput. 19, No. 5, 1625-1645 (1998). Eigenvalues and eigenvectors of a definite symmetric matrix pencil are computed by following homotopy paths from a problem with known solution. It is studied how multiple eigenvalues along the path can be handled. A Rayleigh quotient iteration is used in each homotopy step, and the choice of step length is discussed. Numerical tests are reported, two coming from simple mechanics applications, and one using homotopy through the levels in a multigrid scheme. Reviewer: A.Ruhe (Göteborg) Cited in 8 Documents MSC: 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 65F50 Computational methods for sparse matrices 15A22 Matrix pencils Keywords:homotopy method; symmetric eigenvalue problems; generalized eigenvalue problems; modified eigenvalue problems; perturbation theory; Rayleigh quotient iteration; eigenvectors; symmetric matrix pencil; multiple eigenvalues; multigrid scheme PDFBibTeX XMLCite \textit{T. Zhang} et al., SIAM J. Sci. Comput. 19, No. 5, 1625--1645 (1998; Zbl 0917.65035) Full Text: DOI