Davidson method for eigenpairs and their partial derivatives of generalized eigenvalue problems

摘要

Based on Davidson method for solving generalized eigenvalue problems, a new method for synchro calculation of eigenpairs and their partial derivatives of generalized eigenvalue problems is presented. Eigenpairs and their partial derivatives are computed simultaneously. The equation systems that are solved for eigenvector partial derivatives can be greatly reduced from the original matrix sizes, thus the efficiency of computing eigenvector partial derivatives is improved. Numerical results show that the proposed method is efficient, especially for the large-scale symmetric generalized eigenvalue problems.