Implementing incomplete inverse decomposition on graphical processing units
| Thesis title in Czech: | Implementace neúplného inverzního rozkladu na grafických kartách |
|---|---|
| Thesis title in English: | Implementing incomplete inverse decomposition on graphical processing units |
| Key words: | Přibližná inverze, neúplná faktorizace, grafický procesor |
| English key words: | Approximate inverse, incomplete decomposition, graphical processing unit (GPU) |
| Academic year of topic announcement: | 2012/2013 |
| Thesis type: | diploma thesis |
| Thesis language: | angličtina |
| Department: | Department of Applied Mathematics (32-KAM) |
| Supervisor: | prof. Ing. Miroslav Tůma, CSc. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 18.07.2013 |
| Date of assignment: | 18.07.2013 |
| Confirmed by Study dept. on: | 18.07.2013 |
| Date and time of defence: | 02.09.2013 00:00 |
| Date of electronic submission: | 31.07.2013 |
| Date of submission of printed version: | 02.08.2013 |
| Date of proceeded defence: | 02.09.2013 |
| Opponents: | František Hakl |
| Guidelines |
| Incomplete inverse decompositions represent a set of tools used to precondition iterative methods on high-performance computer architectures. This follows from the fact that an application of the decomposition within a modern Krylov subspace method reduces to one or two matrix-vector multiplications, and such operations are considered as efficiently parallelizable. Nevertheless, the decomposition itself does not parallelize well on multiprocessors. Jan Dědeček should study in his diploma Thesis possibilities to evaluate approximate inverse decompositions on graphical processing units (GPUs). These processors seem to offer an environment that could speed up the construction |
| References |
| M.~Benzi. Preconditioning techniques for large linear systems: a survey., J. Comput. Phys., 182(2):418--477, 2002.
M.Benzi, J.K. Cullum, and M. Tuma. Robust approximate inverse preconditioning for the conjugate gradient method., SIAM J. Sci. Comput., 22(4):1318--1332, 2000. G.H. Golub and C.F. Van Loan., Matrix Computations. 3rd ed., the Johns Hopkins University Press, Baltimore and London, 1996. M.R. Hestenes and E. Stiefel. Methods of conjugate gradients for solving linear systems., J. Res. Nat. Bur. Standards, 49:409--435, 1952. Y.~Saad. Iterative Methods for Sparse Linear Systéme. PWS Publishing Co., Boston, 1996. J. Sanders, E. Kandrot. CUDA by Example: An Introduction to General-Purpose GPU Programming, Addison-Wesley, 2010. |