van der Meulen, Jelmer (2019) Optimizing SOR using derivative-free optimization. Bachelor's Thesis, Mathematics.
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Abstract
When a function is not differentiable, numerical methods can be used to compute the minimum and maximum of a function. These numerical methods are not limited to computing minima of functions, they can also be used to find optimal parameters for iterative methods. This study is mainly concerned with using numerical methods to find optimal relaxation parameters for the iterative method called ”Successive over-relaxation”. It will research the robustness and efficiency of 3 numerical methods called ”The Downhill Simplex Method”, ”Powell’s Method” and ”Simulated Annealing”. These 3 methods have a fundamentally different approach to finding minima and hence will give different results when applied to SOR. In this study we will see that Powell’s Method is not suitable for finding optimal parameters for SOR. Simulated Annealing does well, but is so computationally expensive that it is useless in many situations. The Downhill Simplex Method turns out to be by far the best optimization method for our problem, as it is both the fastest and the most robust method.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Luppes, R. and Sterk, A.E. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 05 Jul 2019 |
| Last Modified: | 09 Jul 2019 09:31 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/19870 |
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