Lanczos-subspace method for generalized eigenproblems

Orthogonality of the Lanczos vectors is lost during iteration owing to the attraction of the round-off errors by some initially found Lanczos vectors, and reorthogonalization is required. An economical and stable method of reorthogonalization by subspace iteration is introduced. The Lanczos vectors without reorthogonalization area taken as initial trial vectors in the subspace method to produce the required eigensolutions. The operation counts of the combined method compare favorably with the Lanczos method with full reorthogonalization for the same accuracy of solutions. Application of the Strum sequence check is recommended to make sure that no solutions are missed in the required spectrum.