Existence Verification for Singular Zeros of Complex Nonlinear Systems

DOI10.1137/S0036142999361074zbMath0986.65054OpenAlexW2087518360MaRDI QIDQ4509687

Arnold Neumaier, Jianwei Dian, Ralph Baker Kearfott

Publication date: 19 October 2000

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0036142999361074

zbMATH Keywords

numerical examplestopological degreeinterval computationscomplex nonlinear systemsinterval-analysissingular Jacobians

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Degree, winding number (55M25) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05)

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Existence verification for singular and nonsmooth zeros of real nonlinear systems ⋮ Solving interval constraints by linearization in computer-aided design ⋮ Intermediate value theorem for simplices for simplicial approximation of fixed points and zeros ⋮ 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 ⋮ OPTIMAL INVESTMENT STRATEGY VIA INTERVAL ARITHMETIC ⋮ Rigorous verification of feasibility ⋮ On isolation of simple multiple zeros and clusters of zeros of polynomial systems ⋮ Generalization of the Bolzano theorem for simplices

Uses Software

• INTOPT_90