A new divide and conquer algorithm for real symmetric band generalized eigenvalue problem

In this paper we present a new divide and conquer algorithm for solving a real symmetric band generalized eigenvalue problem under a distributed environment. This algorithm computes generalized eigenpairs of a real symmetric band matrix pair using the divide and conquer method combined with multisection and generalized Rayleigh quotient iteration. Theoretical analysis and numerical experiments prove that this algorithm is better than the classic method DSBGVX in LAPACK when the scale of matrices is large enough. During parallel computing, there is little communication between processors, so high speedup can be expected.