Inexact preconditioning for iterative methods
| Thesis title in Czech: | Inexact preconditioning for iterative methods |
|---|---|
| Thesis title in English: | Inexact preconditioning for iterative methods |
| Key words: | iterační metody pro řešení soustav lineárních algebraických rovnic, výkonné počítačové architektury, zpětná stabilita |
| English key words: | iterative methods, linear algebraic equations, High-Performance computing, preconditioning, numerical linear algebra, finite precision |
| Academic year of topic announcement: | 2019/2020 |
| Thesis type: | dissertation |
| Thesis language: | |
| Department: | Department of Numerical Mathematics (32-KNM) |
| Supervisor: | Erin Claire Carson, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 20.02.2020 |
| Date of assignment: | 20.02.2020 |
| Confirmed by Study dept. on: | 13.10.2020 |
| Guidelines |
| We consider the use of Krylov subspace methods for solving square linear systems Ax = b
in an iterative fashion. It is standard practice to use preconditioning in order to reduce the number of iterations, which involves solving a transformed linear system with theoretically better numerical properties. There is a complicated tradeoff between the cost per iteration associated with using a particular preconditioner and the resulting convergence rate. In general, we expect the cost per iteration to increase as the number of iterations decrease. Investigating this complicated tradeoff for various iterative methods and applications, in both theory and practice, will be the goal of this project. |
| References |
| Y. Saad. ILUT: A dual threshold incomplete LU factorization. Numer. Lin. Alg. Appl.,
1(4):387{402, 1994. J. Liesen and Z. Strakos. Krylov subspace methods: principles and analysis. Oxford University Press, 2012. A. Greenbaum. Behavior of slightly perturbed Lanczos and conjugate-gradient recurrences. Lin. Alg. Appl., 113:7-63, 1989. Rozložník, Miroslav. Saddle-point problems and their iterative solution. Birkhäuser, 2018. Benzi, Michele. "Preconditioning techniques for large linear systems: a survey." Journal of computational Physics 182.2 (2002): 418-477. Saad, Yousef. Iterative methods for sparse linear systems. Vol. 82. SIAM, 2003. Elman, Howard C. "A stability analysis of incomplete LU factorizations." Mathematics of Computation (1986): 191-217. |
| Preliminary scope of work in English |
| The goal of the work is to study the convergence and stability properties of iterative methods subject to inexactness in preconditioning and design of inexact preconditioning techniques suitable for high-performance computing. |