Numerical Methods for Roots of Polynomials - Part II: Chapter 8. Graeffe’s Root-Squaring Method
- ISBN-10
- 0128076984
- ISBN-13
- 9780128076989
- Series
- Numerical Methods for Roots of Polynomials - Part II
- Category
- Mathematics
- Pages
- 728
- Language
- English
- Published
- 2013-07-19
- Publisher
- Elsevier Inc. Chapters
- Authors
- J.M. McNamee, V.Y. Pan
Description
We discuss Graeffes’s method and variations. Graeffe iteratively computes a sequence of polynomialsso that the roots of are those of raised to the power . Then the roots of can be expressed in terms of the coefficients of . Special treatment is given to complex and/or multiple modulus roots. A method of Lehmer’s finds the argument as well as the modulus of the roots, while other authors show how to reduce the danger of overflow. Variants such as the Chebyshev-like process are discussed. The Graeffe iteration lends itself well to parallel processing, and two algorithms in that context are described. Error estimates are given, as well as several variants.
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- 2013-07-19
- 728 pages
- Ebook
- Elsevier Inc. Chapters
-
- 2013-07-19
- 728 pages
- Ebook
- Elsevier Inc. Chapters
-
- 2013-07-19
- 728 pages
- Ebook
- Elsevier Inc. Chapters
-
- 2013-07-19
- 728 pages
- Ebook
- Elsevier Inc. Chapters
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