Parallel region-preserving multisection method for solving generalized eigenproblem

Abstract

The parallel multisection method for solving algebraic eigenproblem has been presented in recent years with the developing of the parallel computers but all the research work is limited in standard eigenproblem of symmetric tridiagonal matrix. The multisection method for solving generalized eigenproblem applied significantly in many secience and engineering domains has not been studied. The parallel region-preserving multisection method (PRM for shotr) for solving generalized eigenproblem of large sparse real symmetric matrix is presented in this paper. This method not only retains the advantages of the conventional determinant search method (DS for short), but also overcomes its disadvantages such as leaking roots and disconvergence. We tested the method on the YH-1 vector computer, and compared with the parallel region-preserving determinant search method (parallel region-preserving bisection method) (PRB for short). The numerical results show that PRM has a higher speed-up, for instance it attains the speed-up of 7.7 when the scale of the problem is 2114 and the eigenpair found is 3; and PRM is superior to PRB when scale of the problem is large.