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Schur-monotonic Semi-separable Approximations of Symmetric Positive Definite Matrices
Applied Math| Speaker: | Ming Gu, University of California, Berkeley |
| Location: | 1147 MSB |
| Start time: | Fri, Apr 28 2006, 4:10PM |
Abstract: For a given symmetric positive definite matrix A, we develop a fast and backward stable algorithm to approximate A by a symmetric semi-separable matrix, accurate to any prescribed tolerance. In addition, our algorithm guarantees the positive-definiteness of the semi-separable matrix by embedding an approximation strategy inside the Cholesky factorization procedure to ensure that each Schur complement during the Cholesky factorization is more positive definite after approximation. We will present experimental numerical results and discuss potential implications of this work. Joint work with S. Chandrasekaran of UCSB, X. S. Li of LBNL and P. S. Vassilevski of LLNB.