抄録
An effective and practical Lanczos method is presented for large generalized eigenproblems. The number of Lanczos vectors is determined based on the current relation between the number of vectors generated and the number of converged eigenvalues. Based on the CPU time of generating vectors and the triangular factorization, it is judged whether shifting to accelerate the convergence should be applied or not. The shift value is chosen so that the convergence rate of unconverged eigenvalues is larger in the next stage. The error bounds of eigenvalues are formulated for a good choice of the shift in Sturm sequence check. The procedure is implemented in the ADINA program, and it is compared with the subspace method and the accelerated subspace method in computational efficiency. The results of some sample solutions show the presented Lanczos method is one time to ten times faster in calculation than the subspace method and the accelerated subspace method.
