Application of Support Vector Regression in Krylov Solvers
| Autor: | Maharani Abu Bakar, Nur Fadhilah Ibrahim, Rehana Thalib |
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| Rok vydání: | 2021 |
| Předmět: |
Sequence
General Computer Science Iterative method Computer science 0211 other engineering and technologies Extrapolation Lanczos algorithm 020101 civil engineering 02 engineering and technology System of linear equations 0201 civil engineering Support vector machine Lanczos resampling 021105 building & construction Applied mathematics Electrical and Electronic Engineering Interpolation |
| Zdroj: | Annals of Emerging Technologies in Computing. 5:178-186 |
| ISSN: | 2516-029X 2516-0281 |
| DOI: | 10.33166/aetic.2021.05.022 |
| Popis: | Support vector regression (SVR) is well known as a regression or prediction tool under the Machine Learning (ML) which preserves all the key features through the training data. Different from general prediction, here, we proposed SVR to predict the new approximate solutions after we generated some iterates using an iterative method called Lanczos algorithm, one class of Krylov solvers. As we know that all Krylov solvers, including Lanczos methods, for solving the high dimensions of systems of linear equations (SLEs) problems experiences breakdown which causes the sequence of the iterates is incomplete, or the good approximate solution is never reached. By assuming that some iterates exist after the breakdown, then we could predict what they are. It is realized by learning the previous iterates generated by the Lanczos solvers, which is also called the training data. The SVR is then used to predict the next iterate which is expected the sequence now has similar property as the previous one before breaking down. Furthermore, we implemented the hybrid SVR-Lanczos (or SVR-L) in the restarting frame work, then it is called as hybrid restarting-SVR-L. The idea behind the restarting is that one time running hybrid SVR-L cannot obtain a good approximate solution with small residual norm. By taking one iterate which is resulted by the hybrid SVR-L, putting it as the initial guess, will give us the better solution. To test our idea of prediction of SLEs solutions, we also used the regular regression and compared with the SVR. Numerical results are presented and compared between these two predictors. Lastly, we compared our proposed method with existing interpolation and extrapolation methods to predict the approximate solution of SLEs. The results showed that our restarting SVR-L performed better compared with the regular regression. |
| Databáze: | OpenAIRE |
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