Univariate Polynomials: Nearly Optimal Algorithms for Numerical Factorization and Root-finding
نویسندگان
چکیده
منابع مشابه
Univariate Polynomials: Nearly Optimal Algorithms for Numerical Factorization and Root-finding
To approximate all roots (zeros) of a univariate polynomial, we develop two effective algorithms and combine them in a single recursive process. One algorithm computes a basic well isolated zero-free annulus on the complex plane, whereas another algorithm numerically splits the input polynomial of the nth degree into two factors balanced in the degrees and with the zero sets separated by the ba...
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We seek the solution of banded, Toeplitz, Hankel, Vandermonde, Cauchy and other structured linear systems of equations with integer coefficients. By combining Hensel’s symbolic lifting with either divide-and-conquer algorithms or numerical iterative refinement, we unify the solution for all these structures. We yield the solution in nearly optimal randomized Boolean time, which covers both solu...
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Polynomial factorization in conventional sense is an ill-posed problem due to its discontinuity with respect to coefficient perturbations, making it a challenge for numerical computation using empirical data. As a regularization, this paper formulates the notion of numerical factorization based on the geometry of polynomial spaces and the stratification of factorization manifolds. Furthermore, ...
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Root isolation of univariate polynomials is one of the fundamental problems in computational algebra. It aims to find disjoint regions on the real line or complex plane, each containing a single root of a given polynomial, such that the union of the regions comprises all roots. For root solving over the field of complex numbers, numerical methods are the de facto standard. They are known to be ...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2002
ISSN: 0747-7171
DOI: 10.1006/jsco.2002.0531