A comparison of point and ball iterations in the contractive mapping case

DOI10.1007/BF02238651zbMath0815.65075OpenAlexW36896395MaRDI QIDQ1195796

Xingzhong Shi, Zong Ben Xu

Publication date: 13 January 1993

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02238651

zbMATH Keywords

sensitivitycomputational complexityglobal convergencenumerical examplesefficiencyfixed point equationprecisioncontractive mappingregion contraction algorithmball algorithmsBanach contraction mapping theoremcomputational existence theorem

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Interval and finite arithmetic (65G30) Numerical solutions to equations with nonlinear operators (65J15) Complexity and performance of numerical algorithms (65Y20)

Related Items

An optimal ball algorithm for fixed point equations, The optimal ball algorithm for nonlinear equations of quasi-strongly monotone operators, Circumscribed ellipsoid algorithm for fixed-point problems

Cites Work

• Ball algorithms for constructing solutions of nonlinear operator equations
• Geometric estimation of fixed points of Lipschitzian mappings. II
• A Globally Convergent Ball Newton Method
• A Computational Ball Test for the Existence of Solutions to Nonlinear Operator Equations
• A Comparison of the Existence Theorems of Kantorovich and Moore
• A Lipschitz Condition Preserving Extension for a Vector Function
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