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

@article{Xia2010RobustAC,
title={Robust Approximate Cholesky Factorization of Rank-Structured Symmetric Positive Definite Matrices},
author={Jianlin Xia and Ming Gu},
journal={SIAM J. Matrix Anal. Appl.},
year={2010},
volume={31},
pages={2899-2920}
}
• Published 1 July 2010
• Computer Science
• SIAM J. Matrix Anal. Appl.
Given a symmetric positive definite matrix $A$, we compute a structured approximate Cholesky factorization $A\approx\mathbf{R}^{T}\mathbf{R}$ up to any desired accuracy, where $\mathbf{R}$ 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…

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