Efficient Parallel Out-of-Core Implementation of the Cholesky Factorization

In this paper we describe two efficient parallel out-of-core implementations of the Cholesky factorization. We Use the Parallel Out-of-Core Linear Algebra Package (POOCLAPACK) as an extension to the Parallel Linear AIgebra Package (PLAPACK) to implement our out-of-core algorithms. The first algorithm uses in-core kernels with additional code to manage the I/0. This is the classical approach to out-of-core implementations of the Cholesky factorization. Our second algorithm adds an out-of-core implementation of the triangular solve with multiple right hand sides, which doesn''t simply bring code in-core and run the in-core algorithm. This algorithm has the added benefit of requiring fewer copies of the matrix to be in-core at one time, thus allowing more of the matrix to be in-core at one time. Despite the extreme simplicity of POOCLAPACK and our out-of-core algorithm, the out-of-core Cholesky factorization implementation is shown to achieve in excess of 80% of peak performance on a 64 node configuration of the Cray T3E-600.

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