Computation of Topological Degree Using Interval Arithmetic, and Applications

DOI10.2307/2153402zbMath0798.55002OpenAlexW1977804942MaRDI QIDQ4286593

Oliver Aberth

Publication date: 8 November 1994

Full work available at URL: https://doi.org/10.2307/2153402

zbMATH Keywords

topological degreeinterval arithmeticbisection method

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Degree, winding number (55M25)

Related Items (6)

A numerical verification method to specify homoclinic orbits as application of local Lyapunov functions ⋮ Handling polynomial and transcendental functions in SMT via unconstrained optimisation and topological degree test ⋮ Verifying topological indices for higher-order rank deficiencies ⋮ On the complexity of isolating real roots and computing with certainty the topological degree ⋮ Effective topological degree computation based on interval arithmetic ⋮ Quasi-decidability of a fragment of the first-order theory of real numbers

Uses Software

• PNM

Cites Work

• Computing the topological degree of a mapping in \(R^n\)
• An efficient degree-computation method for a generalized method of bisection
• Abstract Generalized Bisection and a Cost Bound
• Interval Methods for Systems of Equations
• The Calculation of the Topological Degree by Quadrature
• A two-dimensional analogue to the method of bisections for solving nonlinear equations
• A Three-Dimensional Analogue to the Method of Bisections for Solving Nonlinear Equations
• Precise computation using range arithmetic, via C++
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