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

  title={Robust Approximate Cholesky Factorization of Rank-Structured Symmetric Positive Definite Matrices},
  author={Jianlin Xia and Ming Gu},
  journal={SIAM J. Matrix Anal. Appl.},
  • J. Xia, M. Gu
  • 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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