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Hussam Al Daas, STFC, Rutherford Appleton Laboratory, Two-level Nyström—Schur preconditioner for symmetric positive definite matrices

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April 13 | 3:00 pm - 4:00 pm EDT

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Randomized methods are becoming increasingly popular in numerical linear algebra. However, few attempts have been made to use them in developing preconditioners. Our interest lies in solving large-scale sparse symmetric positive definite linear systems of equations where the system matrix is preordered to doubly bordered block diagonal form (for example, using a nested dissection ordering). We investigate the use of randomized methods to construct high quality preconditioners. In particular, we propose a new and efficient approach that employs Nyström’s method for computing low rank approximations to develop robust algebraic two-level preconditioners. Construction of the new preconditioners involves iteratively solving a smaller but denser symmetric positive definite Schur complement system with multiple right-hand sides. Numerical experiments on problems coming from a range of application areas demonstrate that this inner system can be solved cheaply using block conjugate gradients and that using a large convergence tolerance to limit the cost does not adversely affect the quality of the resulting Nyström–Schur two-level preconditioner.

This is a joint work with Tyrone Rees and Jennifer Scott from Rutherford Appleton Laboratory.

Host Arvind Saibaba



April 13

3:00 pm - 4:00 pm
Event Category: