Loading Events

Department of Mathematics Calendar

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

  • This event has passed.
April 13 | 3:00 pm - 4:00 pm EDT

Event Navigation

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

Details


Date

April 13

Time
3:00 pm - 4:00 pm
Event Category:
Location
Zoom