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Computing 24, 299--313 (1980) Computing 9 bySpringer-Verlag1980

Summary: Computing 24, 299--313 (1980) Computing
9 bySpringer-Verlag1980
The Fastest Exact Algorithms for the Isolation of
the Real Roots of a Polynomial Equation
A. G. Akritas, Athens
Received March 9, 1979; revised July 22, 1979,and November 22, 1979
Abstract -- Zusammenfassung
The Fastest Exact Algorithms for the Isolation of the Real Roots of a Polynomial Equation. This paper
discusses a set of algorithms which, givena polynomialequation with integer coefficients and without
any multiple roots, uses exact (infinite precision) integer arithmetic and the Vincent-Uspensky-
Akritas theorem to compute intervals containing the real roots of the polynomial equation.
Theoretical computing time bounds are developed for these algorithms which are proven to be
the fastest existing; this fact is also verified by the empirical results which are included in this article.
Die schnellsten exakten Algorithmen zur Isolierung der reellen Nullstellen yon Polynomen. Es werden
einige Algorithmen diskutiert, die unter Verwendung exakter ganzzahliger Arithmetik und des
Vincent-Uspensky-Akritas-Theorems ftir ein gegebenes Polynom mit ganzzahligen Koeffizienten
und ohne mehrfache Wurzeln Intervalle berechnen, die die reellen Nullstellen des Polynoms ent-
halten. Fiir diese Algorithmen werden theoretische Rechenzeitschranken entwickett, und es wird
bewiesen und durch empirische Resultate belegt, dab diese Algorithmen die schnellsten unter den
bisher existierenden sind.


Source: Akritas, Alkiviadis G. - Department of Computer and Communication Engineering, University of Thessaly


Collections: Computer Technologies and Information Sciences