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Precise Numerical Analysis

- Book -
 

Author(s)
Oliver Aberth

Year
1988

Publisher
William Brown

Abstract
Aberth addresses elementary issues of precise floating point computations using variable precision range arithmetic. Numbers are represented as a variable precision number ± a range. Rational arithmetic is also considered. Chapters are devoted to

  1. rootfinding,
  2. polynomial rootfinding,
  3. numerical linear algebra,
  4. differentiation and integration, and
  5. ordinary differential equations
Differentiation is handled by a codelist approach like [Rall1981ADT], and applications to Taylor series are given. Interval techniques for ordinary differential equations are based on using an a priori bound to capture remainder terms. Several methods are illustrated, including Taylor series methods.

AD Theory and Techniques
General

BibTeX
@BOOK{
         Aberth1988PNA,
       AUTHOR = "Aberth, Oliver",
       TITLE = "Precise Numerical Analysis",
       PUBLISHER = "William Brown",
       ADDRESS = "Dubuque, Iowa",
       YEAR = "1988",
       COMMENT = "Text for a one semester, junior level course in numerical analysis. Includes PC disk
         with software written in PBASIC. Sound introductory level discussion of code lists and error capture
         techniques.",
       KEYWORDS = "general numerical analysis; interval techniques; differentiation arithmetic;
         variable precision arithmetic; linear algebra; differentiation; integration; ordinary differential
         equations.",
       ABSTRACT = "Aberth addresses elementary issues of precise floating point computations using
         variable precision range arithmetic. Numbers are represented as a variable precision number
         $\pm$ a range. Rational arithmetic is also considered. Chapters are devoted to
         \begin{enumerate} \item rootfinding, \item polynomial rootfinding, \item
         numerical linear algebra, \item differentiation and integration, and \item ordinary
         differential equations.\end{enumerate} Differentiation is handled by a codelist approach like
         [Rall1981ADT], and applications to Taylor series are given. Interval techniques for ordinary
         differential equations are based on using an {\it a priori\/} bound to capture remainder
         terms. Several methods are illustrated, including Taylor series methods.",
       ad_theotech = "General"
}


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