Isolator Polynomials

Thomas W. Sederberg and Geng-Zhe Chang

Chapter 32 in Algebraic Geometry and its Applications, 1994, pp 507-512 from Springer

Abstract: Abstract This paper explores the problem of isolating the real roots of a polynomial p(x) with real coefficients, that is, of locating intervals which contain exactly one real root of p. A new solution to this problem is presented, consisting of finding a pair of auxiliary polynomials whose set of combined real roots contain at least one value in every closed interval defined by each pair of adjacent real roots in p. It is shown that any member of the polynomial remainder sequence generated by p and p′ can serve as one of these auxiliary polynomials.

Keywords: Real Root; Multiple Root; Algebraic Computation; Real Coefficient; Float Point Arithmetic (search for similar items in EconPapers)
Date: 1994
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DOI: 10.1007/978-1-4612-2628-4_32

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