On flexible block Chebyshev-Davidson method for solving symmetric generalized eigenvalue problems

In a recent work (J. Sci. Comput. 85 (2020), no. 3), the author generalized the Chebyshev-Davidson method appeared in standard eigenvalue problems to symmetric generalized eigenvalue problems. The theoretical derivation indicates that the Chebyshev-Davidson method for symmetric generalized eigenvalue problems only admits local convergence; thus, in this paper, we adopt a flexible strategy to improve the global convergence and to save number of iteration steps. Moreover, the deflation technique used for computing several eigenpairs in the proposed Chebyshev-Davidson method cannot be implemented in parallel; therefore, we construct a flexible block Chebyshev-Davidson method for computing several eigenpairs of symmetric generalized eigenvalue problems. The block implementation is important in scientific computing since it allows parallelism and efficient use of local memory. Numerical experiments are carried out to show great superiority and robustness over some state-of-the-art iteration methods.