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SIAMMAX
2010

Robust Approximate Cholesky Factorization of Rank-Structured Symmetric Positive Definite Matrices

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Robust Approximate Cholesky Factorization of Rank-Structured Symmetric Positive Definite Matrices
Abstract. Given a symmetric positive definite matrix A, we compute a structured approximate Cholesky factorization A RT R up to any desired accuracy, where R is an upper triangular hierarchically semiseparable (HSS) matrix. The factorization is stable, robust, and efficient. The method compresses off-diagonal blocks with rank-revealing orthogonal decompositions. In the meantime, positive semidefinite terms are automatically and implicitly added to Schur complements in the factorization so that the approximation RT R is guaranteed to exist and be positive definite. The approximate factorization can be used as a structured preconditioner which does not break down. No extra stabilization step is needed. When A has an off-diagonal low-rank property, or when the off-diagonal blocks of A have small numerical ranks, the preconditioner is data sparse and is especially efficient. Furthermore, the method has a good potential to give satisfactory preconditioning bounds even if this low-rank prop...
Jianlin Xia, Ming Gu
Added 21 May 2011
Updated 21 May 2011
Type Journal
Year 2010
Where SIAMMAX
Authors Jianlin Xia, Ming Gu
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