Chebyshev polynomials involved in the Householder's method for square roots
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909452149456896 |
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| author | Dijoux, Yann |
| author_facet | Dijoux, Yann |
| contents | The Householder's method is a root-find algorithm which is a natural extension of the methods of Newton and Halley. The current paper mostly focuses on approximating the square root of a positive real number based on these methods. The resulting algorithms can be expressed using Chebyshev polynomials. An extension to the nth root is also proposed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04703 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chebyshev polynomials involved in the Householder's method for square roots Dijoux, Yann General Mathematics 00A05 The Householder's method is a root-find algorithm which is a natural extension of the methods of Newton and Halley. The current paper mostly focuses on approximating the square root of a positive real number based on these methods. The resulting algorithms can be expressed using Chebyshev polynomials. An extension to the nth root is also proposed. |
| title | Chebyshev polynomials involved in the Householder's method for square roots |
| topic | General Mathematics 00A05 |
| url | https://arxiv.org/abs/2501.04703 |