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On the homotopy method for perturbed symmetric generalized eigenvalue problems. (English) Zbl 0917.65035
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.
MSC:
65F15Eigenvalues, eigenvectors (numerical linear algebra)
65F50Sparse matrices (numerical linear algebra)
15A22Matrix pencils