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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.18816 |
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| _version_ | 1866915151254388736 |
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| author | Moshagen, Thilo |
| author_facet | Moshagen, Thilo |
| contents | In this paper a fixed-point solver for mappings from a Simplex into itself that is gradient-free, global and requires $d$ function evaluations for halvening the error is presented, where $d$ is the dimension. It is based on topological arguments and uses the constructive proof of the Mazurkewicz-Knaster-Kuratowski lemma as used as part of the proof for Brouwers Fixed-Point theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18816 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global Solver based on the Sperner-Lemma and Mazurkewicz-Knaster-Kuratowski-Lemma based proof of the Brouwer Fixed-Point Theorem Moshagen, Thilo Numerical Analysis Functional Analysis 26B12, 46N10, 47H10, 65H10, 65H20 G.1.5 In this paper a fixed-point solver for mappings from a Simplex into itself that is gradient-free, global and requires $d$ function evaluations for halvening the error is presented, where $d$ is the dimension. It is based on topological arguments and uses the constructive proof of the Mazurkewicz-Knaster-Kuratowski lemma as used as part of the proof for Brouwers Fixed-Point theorem. |
| title | Global Solver based on the Sperner-Lemma and Mazurkewicz-Knaster-Kuratowski-Lemma based proof of the Brouwer Fixed-Point Theorem |
| topic | Numerical Analysis Functional Analysis 26B12, 46N10, 47H10, 65H10, 65H20 G.1.5 |
| url | https://arxiv.org/abs/2407.18816 |