Bounds for positive roots of polynomials
نویسندگان
چکیده
منابع مشابه
Improved Computation of Bounds for Positive Roots of Polynomials
A new lower bound for computing positive roots of polynomial equations is proposed. We discuss a twostage algorithm for computing positive roots of polynomial equations. In the first stage, we use the continued fraction method based on Vincent’s theorem, which employs the lower bound of real roots, for isolating the positive roots into intervals. In the second stage, we apply a bisection method...
متن کاملOn Bounds for Real Roots of Polynomials
The computation of the real roots of univariate polynomials with real coefficients is done using several algorithmic devices. Many of them are based on the isolation of the real roots, i.e. the computation of a finite number of intervals with the property that each of them contains exactly one root. For that one of the steps is that of computing bounds for the roots. This can be realized using ...
متن کاملA Comparison of Various Methods for Computing Bounds for Positive Roots of Polynomials
The recent interest in isolating real roots of polynomials has revived interest in computing sharp upper bounds on the values of the positive roots of polynomials. Until now Cauchy’s method was the only one widely used in this process. Ştefănescu’s recently published theorem offers an alternative, but unfortunately is of limited applicability as it works only when there is an even number of sig...
متن کاملGale duality bounds for roots of polynomials with nonnegative coefficients
We bound the location of roots of polynomials that have nonnegative coefficients with respect to a fixed but arbitrary basis of the vector space of polynomials of degree at most d. For this, we interpret the basis polynomials as vector fields in the real plane, and at each point in the plane analyze the combinatorics of the Gale dual vector configuration. We apply our technique to bound the loc...
متن کاملRoots of polynomials with positive coefficients
We describe the limit zero distributions of sequences of polynomials with positive coefficients. We also characterize the polynomials with real coefficients for which some power has positive coefficients. MSC Primary: 30C15, 26C10, secondary: 31A05.
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1986
ISSN: 0377-0427
DOI: 10.1016/0377-0427(86)90096-8