Interval methods for fixed-point problems

DOI10.1080/01630568708816225zbMath0586.65046OpenAlexW2154782729MaRDI QIDQ3711672

Louis B. Rall

Publication date: 1987

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630568708816225

zbMATH Keywords

numerical exampleexistenceinterval analysisinterval iterationfixed point problempartially-ordered spaces

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10) Interval and finite arithmetic (65G30) Numerical solutions to equations with nonlinear operators (65J15) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07)

Cites Work

• Mean value forms in interval analysis
• Interval extensions and interval iterations
• Solution of finite systems of equations by interval iteration
• Vergleich intervallarithmetischer Iterationsverfahren
• Stability and convergence of monotonic algorithms
• Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken
• Mean Value and Taylor Forms in Interval Analysis
• A Comparison of the Existence Theorems of Kantorovich and Moore
• Integration of Interval Functions
• Integration of Interval Functions: II. The Finite Case
• Contraction mappings in interval analysis
• Safe Starting Regions for Iterative Methods
• Numerical Integration and the Solution of Integral Equations by the Use of Riemann Sums
• A Note on the Convergence of Newton’s Method
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