Engineering and physics applications frequently give rise to generalized eigenvalue problems of the form A x = \lambda B x, where A is Hermitian and B is Hermitian positive definite. In structural dynamics, A and B are respectively the stiffness and mass matrices, and for discretizations of the time-independent Schroedinger equation, they are the Hamiltonian and overlap matrices. When a large percentage of the eigenpairs are sought, the first steps in the process are typically to find the Cholesky factor of B and transform the problem into a Hermitian standard eigenvalue problem. Unfortunately, the LAPACK and ScaLAPACK approach for this transformation is inherently unscalable and quickly becomes the dominant portion of the eigensolution. A new approach is demonstrated that yields a 20x speedup on two racks of Blue Gene/P.

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