Efficient Numerical Validation of Solutions of Nonlinear Systems

DOI10.1137/0731013zbMath0796.65068OpenAlexW2057612756MaRDI QIDQ4294767

Florian A. Potra, A. Gienger, G. E. Alefeld

Publication date: 10 October 1994

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/84e135f988ba15adb9e97c0d8429a48e65e906f8

zbMATH Keywords

system of nonlinear equationsKrawczyk operatorinterval vectorstopping criterionKantorovich theoremNewton algorithmnumerical validation of solutions

Mathematics Subject Classification ID

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

Related Items (12)

Numerical validation for an inverse matrix eigenvalue problem ⋮ Enclosing solutions of an inverse Sturm-Liouville problem with finite data ⋮ Formulas for the width of interval products ⋮ Experiences with a method for enclosing solutions of systems of equations ⋮ A verification method for solutions of nonsmooth equations ⋮ A switching-method for nonlinear systems ⋮ Higher order multi-step interval iterative methods for solving nonlinear equations in \(\mathbb R^n\) ⋮ Verification for existence of solutions of linear complementarity problems ⋮ Computational experience with globally convergent descent methods for large sparse systems of nonlinear equations^∗ ⋮ A genetic algorithm with a self-reproduction operator to solve systems of nonlinear equations ⋮ Interval analysis: Theory and applications ⋮ Interval mathematics, algebraic equations and optimization

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