Parallel eigenvalue computation for banded generalized eigenvalue problems

摘要

We consider generalized eigenvalue problems Ax = Bx lambda with a banded symmetric matrix A and a banded symmetric positive definite matrix B. To reduce the generalized eigenvalue problem to standard form Cy = y lambda. the algorithm proposed by Crawford is applied preserving the banded structure in C. We present a parallel implementation of this method for the ELPA library. Performance analysis shows the capabilities of the approach. (C) 2019 Elsevier B.V. All rights reserved.