Tangent Graeffe Iteration
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
1999
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| _version_ | 1866918162988007424 |
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| author | Malajovich, Gregorio Zubelli, Jorge P. |
| author_facet | Malajovich, Gregorio Zubelli, Jorge P. |
| contents | Graeffe iteration was the choice algorithm for solving univariate polynomials in the XIX-th and early XX-th century. In this paper, a new variation of Graeffe iteration is given, suitable to IEEE floating-point arithmetics of modern digital computers. We prove that under a certain generic assumption the proposed algorithm converges. We also estimate the error after N iterations and the running cost. The main ideas from which this algorithm is built are: classical Graeffe iteration and Newton Diagrams, changes of scale (renormalization), and replacement of a difference technique by a differentiation one. The algorithm was implemented successfully and a number of numerical experiments are displayed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_9908150 |
| institution | arXiv |
| publishDate | 1999 |
| record_format | arxiv |
| spellingShingle | Tangent Graeffe Iteration Malajovich, Gregorio Zubelli, Jorge P. Numerical Analysis Graeffe iteration was the choice algorithm for solving univariate polynomials in the XIX-th and early XX-th century. In this paper, a new variation of Graeffe iteration is given, suitable to IEEE floating-point arithmetics of modern digital computers. We prove that under a certain generic assumption the proposed algorithm converges. We also estimate the error after N iterations and the running cost. The main ideas from which this algorithm is built are: classical Graeffe iteration and Newton Diagrams, changes of scale (renormalization), and replacement of a difference technique by a differentiation one. The algorithm was implemented successfully and a number of numerical experiments are displayed. |
| title | Tangent Graeffe Iteration |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/math/9908150 |