This paper describes a method of calculating the Schur complement of a sparse positive definite matrix A. The main idea of this approach is to represent matrix A in the form of an elimination tree using a reordering algorithm like METIS and putting columns/rows for which the Schur complement is needed into the top node of the elimination tree. Any problem with a degenerate part of the initial matrix can be resolved with the help of iterative refinement. The proposed approach is close to the “multifrontal” one which was implemented by Ian Duff and others in 1980s. Schur complement computations described in this paper are available in Intel® Math Kernel Library (Intel® MKL). In this paper we present the algorithm for Schur complement computations, experiments that demonstrate a negligible increase in the number of elements in the factored matrix, and comparison with existing alternatives.
Multifrontal Method, Direct Method, Sparse Linear System, Schur Complement, HPC, Intel® MKL
Kalinkin, A. , Anders, A. and Anders, R. (2015) Schur Complement Computations in Intel® Math Kernel Library PARDISO. Applied Mathematics, 6, 304-311. doi: 10.4236/am.2015.62028.
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