Numerical Methods for Roots of Polynomials - Part II: Chapter 7. Bisection and Interpolation Methods
- ISBN-10
- 0128076976
- ISBN-13
- 9780128076972
- 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 the secant method:where are initial guesses. In the Regula Falsi variation we start with initial guesses and such that ; after an iteration similar to the above we replace either a or b by the new value depending on which of or has the same sign as . Often one of the points gets “stuck,” and several variants such as the Illinois or Pegasus methods and variations are used to “unstick” it. We discuss convergence and efficiency of most of the methods considered. We treat methods involving quadratic of higher order interpolation and rational approximation. We also discuss the bisection method where again and we set . We replace a or b by c according to the sign of as in the Regula Falsi method. Various generalizations are described, including some for complex roots. Finally we consider hybrid methods involving two or more of the previously described methods.
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Other editions
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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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