Complete numerical isolation of real roots in zero-dimensional triangular systems

DOI10.1016/j.jsc.2008.04.017zbMath1169.13017OpenAlexW1964839258MaRDI QIDQ1025386

Chee-Keng Yap, Jin-San Cheng~, Xiao-Shan Gao

Publication date: 18 June 2009

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2008.04.017

zbMATH Keywords

triangular systemevaluation boundreal zero isolationsleeve bound

Mathematics Subject Classification ID

Related Items (13)

Certified numerical real root isolation for bivariate nonlinear systems ⋮ Computing the intersection between a rational parametric curve and a rational parametric surface ⋮ Root isolation of zero-dimensional polynomial systems with linear univariate representation ⋮ Collision and intersection detection of two ruled surfaces using bracket method ⋮ Univariate Real Root Isolation over a Single Logarithmic Extension of Real Algebraic Numbers ⋮ A generic position based method for real root isolation of zero-dimensional polynomial systems ⋮ From approximate factorization to root isolation with application to cylindrical algebraic decomposition ⋮ Univariate real root isolation in an extension field and applications ⋮ Adaptive isotopic approximation of nonsingular curves: The parameterizability and nonlocal isotopy approach ⋮ Homeomorphic approximation of the intersection curve of two rational surfaces ⋮ Certified approximation of parametric space curves with cubic \(B\)-spline curves ⋮ Clustering complex zeros of triangular systems of polynomials ⋮ Ambient Isotopic Meshing for Implicit Algebraic Surfaces with Singularities

Uses Software

• ISOLATE

Cites Work

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• Interval arithmetic in cylindrical algebraic decomposition
• An algorithm for isolating the real solutions of semi-algebraic systems
• Real solution isolation using interval arithmetic
• Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems
• The Method of Resultants for Computing Real Solutions of Polynomial Systems
• Fast Multiple-Precision Evaluation of Elementary Functions
• Cylindrical Algebraic Decomposition I: The Basic Algorithm
• Mathematics of Surfaces XI
• Computer Algebra in Scientific Computing

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