Ten methods to bound multiple roots of polynomials

DOI10.1016/S0377-0427(03)00381-9zbMath1030.65046MaRDI QIDQ1398714

Siegfried Michael Rump

Publication date: 7 August 2003

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

multiple rootsunivariate polynomialsrounding errorscomplexity boundshybrid algorithmbounding roots

Mathematics Subject Classification ID

Related Items (21)

Cauchy-like and Pellet-like results for polynomials ⋮ On Newton-type methods for multiple roots with cubic convergence ⋮ RESOLUTION OF MULTIPLE ROOTS OF NONLINEAR POLYNOMIAL SYSTEMS ⋮ A verified method for bounding clusters of zeros of analytic functions ⋮ A property of the nearly optimal root-bound ⋮ Exact symbolic-numeric computation of planar algebraic curves ⋮ Validated Root Enclosures for Interval Polynomials with Multiplicities ⋮ Flexible Bayesian inference for diffusion processesusing splines ⋮ Enclosing clusters of zeros of polynomials ⋮ On the location of roots of non-reciprocal integer polynomials ⋮ On the convergence condition of generalized root iterations for the inclusion of polynomial zeros ⋮ Computing Enclosures for the Matrix Exponential ⋮ On new higher order families of simultaneous methods for finding polynomial zeros ⋮ A family of root-finding methods with accelerated convergence ⋮ A new and novel method for computing an upper bound on the distance of an approximate zero from an exact zero of a univariate polynomial ⋮ From approximate factorization to root isolation with application to cylindrical algebraic decomposition ⋮ Perturbation bounds for polynomials ⋮ An efficient higher order family of root finders ⋮ A higher order family for the simultaneous inclusion of multiple zeros of polynomials ⋮ Verified error bounds for multiple roots of systems of nonlinear equations ⋮ Sigmoid-like functions and root finding methods

Uses Software

• Matlab
• INTLAB

Cites Work

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