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DTSTART:20210314T070000
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DTSTART;TZID=America/New_York:20210413T150000
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SUMMARY:Hussam Al Daas\, STFC\, Rutherford Appleton Laboratory\, Two-level Nyström—Schur preconditioner for symmetric positive definite matrices
DESCRIPTION: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. \n\nThis is a joint work with Tyrone Rees and Jennifer Scott from Rutherford Appleton Laboratory. \nHost Arvind Saibaba
URL:https://math.sciences.ncsu.edu/event/hussam-al-daas-stfc-rutherford-appleton-laboratory/
LOCATION:Zoom
CATEGORIES:Numerical Analysis Seminar
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