New Combinations of Polynomial Root-Finding Iterations
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arXiv
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| Format: | Preprint |
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2017
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| _version_ | 1866916056613781504 |
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| author | Pan, Victor Y. |
| author_facet | Pan, Victor Y. |
| contents | Some near-optimal polynomial root-finders of 2024-25, based on subdivision iterations, approximate all complex roots of a polynomial or all roots in a fixed Region of Interest in the complex plane. The iterations can be applied to a black box polynomial, represented by an oracle (black box subroutine) for its evaluation rather than in monomial basis - by coefficients. We propose further empirical acceleration, for which we combine these iterations with Ehrlich's (aka Aberth's), Newton's, or Schroeder's. Our combinations of Ehrlich/Newton/Schroeder's and subdivision iterations can be applied to a black box polynomial and promises to support empirical acceleration versus each approach standing alone. A by-product of our study is a natural extension of the Gauss-Lucas theorem, of independent interest. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1705_00729 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | New Combinations of Polynomial Root-Finding Iterations Pan, Victor Y. Numerical Analysis Some near-optimal polynomial root-finders of 2024-25, based on subdivision iterations, approximate all complex roots of a polynomial or all roots in a fixed Region of Interest in the complex plane. The iterations can be applied to a black box polynomial, represented by an oracle (black box subroutine) for its evaluation rather than in monomial basis - by coefficients. We propose further empirical acceleration, for which we combine these iterations with Ehrlich's (aka Aberth's), Newton's, or Schroeder's. Our combinations of Ehrlich/Newton/Schroeder's and subdivision iterations can be applied to a black box polynomial and promises to support empirical acceleration versus each approach standing alone. A by-product of our study is a natural extension of the Gauss-Lucas theorem, of independent interest. |
| title | New Combinations of Polynomial Root-Finding Iterations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/1705.00729 |