A Real Polynomial Decision Algorithm Using Arbitrary-Precision Floating Point Arithmetic

Adam Strzebonski ()
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Adam Strzebonski: Wolfram Research Inc. and Jagiellonian University

A chapter in Developments in Reliable Computing, 1999, pp 337-346 from Springer

Abstract: Abstract We study the problem of deciding whether a system of real polynomial equations and inequalities has solutions, and if yes finding a sample solution. For polynomials with exact rational number coefficients the problem can be solved using a variant of the cylindrical algebraic decomposition (CAD) algorithm. We investigate how the CAD algorithm can be adapted to the situation when the coefficients are inexact, or, more precisely, Mathematica arbitrary-precision floating point numbers. We investigate what changes need to be made in algorithms used by CAD, and how reliable are the results we get.

Keywords: Weak Solution; Error Bound; Input System; Inequality System; Strong Inequality (search for similar items in EconPapers)
Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-1247-7_26

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DOI: 10.1007/978-94-017-1247-7_26

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