Quadratic Speedup for Computing Contraction Fixed Points
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914321387225088 |
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| author | Chen, Xi Li, Yuhao Yannakakis, Mihalis |
| author_facet | Chen, Xi Li, Yuhao Yannakakis, Mihalis |
| contents | We study the problem of finding an $ε$-fixed point of a contraction map $f:[0,1]^k\mapsto[0,1]^k$ under both the $\ell_\infty$-norm and the $\ell_1$-norm. For both norms, we give an algorithm with running time $O(\log^{\lceil k/2\rceil}(1/ε))$, for any constant $k$. These improve upon the previous best $O(\log^k(1/ε))$-time algorithm for the $\ell_{\infty}$-norm by Shellman and Sikorski [SS03], and the previous best $O(\log^k (1/ε))$-time algorithm for the $\ell_{1}$-norm by Fearnley, Gordon, Mehta and Savani [FGMS20]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10296 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quadratic Speedup for Computing Contraction Fixed Points Chen, Xi Li, Yuhao Yannakakis, Mihalis Computational Complexity Data Structures and Algorithms We study the problem of finding an $ε$-fixed point of a contraction map $f:[0,1]^k\mapsto[0,1]^k$ under both the $\ell_\infty$-norm and the $\ell_1$-norm. For both norms, we give an algorithm with running time $O(\log^{\lceil k/2\rceil}(1/ε))$, for any constant $k$. These improve upon the previous best $O(\log^k(1/ε))$-time algorithm for the $\ell_{\infty}$-norm by Shellman and Sikorski [SS03], and the previous best $O(\log^k (1/ε))$-time algorithm for the $\ell_{1}$-norm by Fearnley, Gordon, Mehta and Savani [FGMS20]. |
| title | Quadratic Speedup for Computing Contraction Fixed Points |
| topic | Computational Complexity Data Structures and Algorithms |
| url | https://arxiv.org/abs/2602.10296 |