caa a22 4500 465774474 CHVBK 20180323111938.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF02283694 doi (NATIONALLICENCE)springer-10.1007/BF02283694 Kearfott R. Department of Mathematics, University of Southwestern Louisiana, 70505, Lafayette, Louisiana, USA aut Interval Newton/generalized bisection when there are singularities near roots [Elektronische Daten] [R. Kearfott] Interval Newton methods in conjunction with generalized bisection are important elemetns of algorithms which find theglobal optimum within a specified box X ⊂ ℝn of an objective function ϕ whose critical points are solutions to the system of nonlinear equationsF(X)=0with mathematical certainty, even in finite presision arithmetic. The overall efficiency of such a scheme depends on the power of the interval Newton method to reduce the widths of the coordinate intervals of the box. Thus, though the generalized bisection method will still converge in a box which contains a critical point at which the Jacobian matrix is singular, the process is much more costly in that case. Here, we propose modifications which make the generalized bisection method isolate singular solutions more efficiently. These modifications are based on an observation about the verification property of interval Newton methods and on techniques for detecting the singularity and removing the region containing it. The modifications assume no special structure forF. Additionally, one of the observations should also make the algorithm more efficient when finding nonsingular solutions. We present results of computational experiments. J.C. Baltzer A.G. Scientific Publishing Company, 1990 Nonlinear algebraic systems nationallicence Newton's method nationallicence interval arithmetic nationallicence Gauss-Seidel method nationallicence global optimization nationallicence singularities nationallicence Annals of Operations Research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers 25/1(1990-12-01), 181-196 0254-5330 25:1<181 1990 25 10479 https://doi.org/10.1007/BF02283694 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02283694 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kearfott R. Department of Mathematics, University of Southwestern Louisiana, 70505, Lafayette, Louisiana, USA aut NATIONALLICENCE 773 0- Annals of Operations Research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers 25/1(1990-12-01), 181-196 0254-5330 25:1<181 1990 25 10479 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer