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Circular arithmetic and the determination of polynomial zeros

✍ Scribed by Irene Gargantini; Peter Henrici

Book ID
105182020
Publisher
Springer-Verlag
Year
1971
Tongue
English
Weight
669 KB
Volume
18
Category
Article
ISSN
0029-599X

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πŸ“œ SIMILAR VOLUMES

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Congruence arithmetic algorithms for polynomial real zero determination
✍ Lee E. Heindel πŸ“‚ Article πŸ“… 1974 πŸ› Elsevier Science 🌐 English βš– 903 KB

This paper describes a set of algorithms for isolating the real zeros of a univariate polynomial with integer coefficients. The algorithms employ congruence (modular, finite field) arithmetic and are analogous to a set of integer arithmetic algorithms described by the author in a recent paper. The a

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✍ Stef Graillat πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 330 KB

In the paper, we examine the local behavior of Newton's method in floating point arithmetic for the computation of a simple zero of a polynomial assuming that an good initial approximation is available. We allow an extended precision (twice the working precision) in the computation of the residual.