A framework for existence tests based on the topological degree and homotopy

DOI10.1007/s00211-008-0193-3zbMath1163.65024OpenAlexW2115168475MaRDI QIDQ1006842

Andreas Frommer, Bruno Lang, Thomas Beelitz, Paul R. Willems

Publication date: 26 March 2009

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-008-0193-3

zbMATH Keywords

numerical examplecomparison of methodsKrawczyk operatortopological degreeinterval arithmetichomotopyMoore-Kioustelidis testzeros of nonlinear mappings

Mathematics Subject Classification ID

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

Related Items (1)

Effective topological degree computation based on interval arithmetic

Uses Software

• INTLAB
• INTOPT_90
• GlobSol
• SONIC

Cites Work

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• Proving the existence of zeros using the topological degree and interval arithmetic
• Solving nonlinear systems with least significant bit accuracy
• Rigorous global search: continuous problems
• Epsilon-inflation in verification algorithms
• Improved iteration schemes for validation algorithms for dense and sparse nonlinear systems
• On the proofs of some statements concerning the theorems of Kantorovich, Moore, and Miranda
• On Preconditioners for the Borsuk Existence Test
• A Simple Test for Accuracy of Approximate Solutions to Nonlinear (or Linear) Systems
• Interval Methods for Systems of Equations
• A Test for Existence of Solutions to Nonlinear Systems
• Existence Tests for Solutions of Nonlinear Equations Using Borsuk's Theorem

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