Real Root Isolation of Polynomial Equations Based on Hybrid Computation

DOI10.1007/978-3-662-43799-5_26zbMath1336.65080arXiv1207.3019OpenAlexW1585832896MaRDI QIDQ2799571

Wenyuan Wu, Fei Shen, Bican Xia

Publication date: 12 April 2016

Published in: Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.3019

zbMATH Keywords

algorithmnumerical examplespolynomial systeminterval arithmetichomotopy continuation methodreal root isolationKrawczyk interval iteration

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Interval and finite arithmetic (65G30) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Numerical computation of roots of polynomial equations (65H04)

Related Items (5)

VerifyRealRoots: a Matlab package for computing verified real solutions of polynomials systems of equations and inequalities ⋮ Early Ending in Homotopy Path-Tracking for Real Roots ⋮ Visualizing planar and space implicit real algebraic curves with singularities ⋮ A hybrid procedure for finding real points on a real algebraic set ⋮ Bound the number of limit cycles bifurcating from center of polynomial Hamiltonian system via interval analysis

Uses Software

• INTLAB
• alphaCertified
• DISCOVERER
• ISOLATE

Cites Work

• Unnamed Item
• Root isolation of zero-dimensional polynomial systems with linear univariate representation
• On continued fraction expansion of real roots of polynomial systems, complexity and condition numbers
• Solving zero-dimensional systems through the rational univariate representation
• An algorithm for isolating the real solutions of semi-algebraic systems
• Robust certified numerical homotopy tracking
• Real solution isolation using interval arithmetic
• Newton's method with deflation for isolated singularities of polynomial systems
• Certified Numerical Homotopy Tracking
• Verification methods: Rigorous results using floating-point arithmetic
• Algorithm 921
• Multiple zeros of nonlinear systems
• Introduction to Interval Analysis
• Optimal Error Bounds for the Newton–Kantorovich Theorem
• Solving Real Polynomial Systems with Real Homotopies
• The Numerical Solution of Systems of Polynomials Arising in Engineering and Science

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