- Referenced in 218 articles
- Efficient isolation of polynomial’s real roots. This paper revisits an algorithm isolating the real ... roots of a univariate polynomial using Descartes’ rule of signs. It follows work of Vincent...
- Referenced in 100 articles
- MultRoot - a Matlab package for computing polynomial roots and multiplicities. MultRoot is a collection ... Matlab modules for accurate computation of polynomial roots, especially roots with non-trivial multiplicities ... requires the polynomial coefficients as the only input, and outputs the computed roots, multiplicities, backward ... accuracy on multiple roots without using multiprecision arithmetic, even if the polynomial coefficients are inexact...
- Referenced in 304 articles
- problems, finding the roots of nonlinear equations, integrating ordinary functions, manipulating polynomials, and integrating ordinary...
- Referenced in 333 articles
- roots. Periodic solutions, their Floquet multipliers and connecting orbits are computed using piecewise polynomial collocation...
- Referenced in 77 articles
- Design, analysis, and implementation of a multiprecision polynomial rootfinder. We present the design, analysis ... number of digits of the roots of a polynomial with complex coefficients. The real...
- Referenced in 471 articles
- systems of nonlinear equations (including unconstrained optimization) roots of univariate and multivariate nonlinear equations (simple ... clusters) quadrature for univariate functions univariate polynomial zeros (simple and clusters) interval arithmetic for real...
- Referenced in 43 articles
- MPFI are given: robotics, isolation of polynomial real roots (by an algorithm combining symbolic...
- Referenced in 24 articles
- require finding and counting real roots of polynomials over an algebraic extension ... those polynomials are algebraic numbers. Various algebraic approaches for this real root finding and counting ... that avoids finding and counting real roots of polynomials with non-rational coefficients. We achieve...
- Referenced in 89 articles
- loop detection, matrix interpretation, polynomial interpretation, predictive labeling, recursive SCC, root-labeling, semantic labeling, simple...
- Referenced in 25 articles
- iterated eigenvalue algorithm for approximating roots of univariate polynomials. The author studies an iterative algorithm ... that approximates all roots of a univariate polynomial. The iteration is based on floating-point...
- Referenced in 23 articles
- representing and manipulating the following: Multivariate polynomials with floating-point, multiprecision integer, or multiprecision rational ... coefficients. Algebraic numbers represented as the roots of polynomials within an interval...
- Referenced in 16 articles
- Root isolation for bivariate polynomial systems with local generic position method. A local generic position ... proposed to isolate the real roots of a bivariate polynomial system ... linear combinations of the roots of two univariate polynomial equations ... satisfying certain conditions. The multiplicities of the roots of Σ=0 are the same...
- Referenced in 14 articles
- Minimal and maximal real roots of parametric polynomials using interval analysis In this paper ... interested in parametric polynomials, i.e. polynomials whose coefficients are analytical functions of parameters that ... finding the extremal real roots for the set of polynomials and determining an approximation ... values such that all the polynomials have their root real part in a given range...
- Referenced in 236 articles
- been accomplished on exploiting structure in a polynomial system, in particular its sparsity. In this ... This package features a great variety of root-counting methods among its tools. The outline...
- Referenced in 253 articles
- Numerical Algebraic Geometry. Software for solving polynomial systems. Finds isolated solutions using total-degree start ... power-series endgame to accurately compute singular roots Allows for subfunctions. Allows for witness...
- Referenced in 11 articles
- Computing real roots of real polynomials dots and now for real! Very recent work introduces ... isolating the real roots of a univariate real polynomial. The method combines Descartes? Rule ... test intervals for the existence of roots, Newton iteration to speed up convergence against clusters...
- Referenced in 7 articles
- geometric predicates or on the roots of polynomials characterizing the problem. The reliability ... accurate evaluation of these signs and roots. In this paper, we present a naive precision ... algorithm to compute all the roots of a univariate polynomial to any desired accuracy...
- Referenced in 11 articles
- almost) optimal real-root isolation algorithm. Let f be a univariate polynomial with real coefficients ... widely used for isolating the real roots of f in a given interval. In this ... problem of isolating all real roots of an integer polynomial f of degree ... amortization technique of the standard Mahler-Davenport root bounds to interpret the integral in terms...
- Referenced in 5 articles
- Fourier stability analysis. HURWP for locating polynomial roots necessary in verifying the von Neumann stability...