On interval operators obtained by splitting the Lipschitz matrix

DOI10.1016/0022-247X(88)90108-4zbMath0662.65047OpenAlexW2067422404MaRDI QIDQ1114342

S. H. Smith

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1016/0022-247x(88)90108-4

zbMATH Keywords

convergencenumerical examplesiterative methodsinterval arithmeticComparisonsinterval operatorsenclosure of solutionsGauss-Seidel splittinginclusion monotonicityinterval splittingsJacobi-splittingmidpoint splittingStable fixed points

Mathematics Subject Classification ID

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

Cites Work

• Centered forms and interval operators
• New techniques for the analysis of linear interval equations
• Interval iterations for including a set of solutions
• Interval iteration for zeros of systems of equations
• A class of interval-Newton-operators
• Properties of interval operators
• Interval Newton operators for function strips
• Bounding solutions of systems of equations using interval analysis
• Further results on linear interval equations
• An Interval Arithmetic Approach for the Construction of an Almost Globally Convergent Method for the Solution of the Nonlinear Poisson Equation on the Unit Square
• On the Acceleration of an Interval-Arithmetic Iteration Method
• Krawczyk-Like Algorithms for the Solution of Systems of Nonlinear Equations
• A Quadratically Convergent Krawczyk-Like Algorithm

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