An Improved Verification Algorithm for Nonlinear Systems of Equations Based on the Optimal Rump Interval Operator
In this paper,an improved verification algorithm for solutions of nonlinear systems of equations is proposed based on the Baumann optimal central form.Firstly,the relationship between the Rump interval operator and the Krawczyk interval operator is stud-ied;Secondly,the optimal Rump interval operator is given with the method of construction for the optimal Krawczyk interval operator;And finally,an interval algorithm is designed to verify the existence of solutions of nonlinear systems of equations based on the improved Rump's existence theorem for solutions.Compared with Rump's verification algorithm,both theoretical and numerical experimental results show that the algorithms given in this paper can give the inclusion intervals with the narrowest(or at least the same)width of these solutions.
optimal rump interval operatorBaumann optimal central formtrusted veri-fication
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