The Krawczyk operator and Kantorovich's theorem

DOI10.1016/0022-247X(90)90053-IzbMath0717.65028MaRDI QIDQ2638725

Arnold Neumaier, Zu He Shen

Publication date: 1990

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

comparisonKrawczyk operatorinterval arithmeticKantorovich's test

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Interval and finite arithmetic (65G30)

Related Items (9)

A method for global minimization of functions using the Krawczyk operator ⋮ Computer assisted proofs for transverse collision and near collision orbits in the restricted three body problem ⋮ A method to find all the roots of the system of nonlinear algebraic equations based on the Krawczyk operator ⋮ Decompostition of arithmetic expressions to improve the behavior of interval iteration for nonlinear systems ⋮ On the proofs of some statements concerning the theorems of Kantorovich, Moore, and Miranda ⋮ Exclusion regions for parameter-dependent systems of equations ⋮ On the comparison of a Kantorovich-type and Moore theorems ⋮ Method for localizing the zeros of analytic functions based on the Krawczyk operator ⋮ Interval analysis on directed acyclic graphs for global optimization

Cites Work

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• Existence of solutions of piecewise differentiable systems of equations
• Interval Slopes for Rational Functions and Associated Centered Forms
• A Comparison of the Existence Theorems of Kantorovich and Moore
• Perturbation Bounds for Nonlinear Equations
• A Test for Existence of Solutions to Nonlinear Systems
• A Computational Test for Convergence of Iterative Methods for Nonlinear Systems

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