The spectral transformation Lánczos method for the numerical solution of large sparse generalized symmetric eigenvalue problems

摘要: A new algorithm is developed which computes a specified number of eigenvalues in any part the spectrum generalized symmetric matrix eigenvalue problem. It uses linear system routine (factorization and solution) as tool for applying Lanczos to shifted inverted The determines sequence shifts checks that all get computed intervals between them. shown each shift several eigenvectors will converge after very few steps algorithm, most effective combination runs determined different sizes sparsity properties matrices. For large problems operation counts are about five times smaller than traditional subspace iteration methods. Tests on numerical example, arising from finite element computation nuclear power piping system, reported, it how performance predicted bears out practical situation.