Journal ArticleDOI
A globally convergent interval method for computing and bounding real roots
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TLDR
This extended interval Newton method will isolate and bound all the real roots of a continuously differentiable function in a given interval and it is proved that the method never fails to converge.Abstract:
In this paper, we extend the interval Newton method to the case where the interval derivative may contain zero. This extended method will isolate and bound all the real roots of a continuously differentiable function in a given interval. In particular, it will bound multiple roots. We prove that the method never fails to converge.read more
Citations
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Book ChapterDOI
Interval Analysis in the Extended Interval Space IR
TL;DR: In this paper, the extended interval space IR can be used to write formulas, theorems, and proofs in a closed form, without using the left and right interval bounds.
Journal ArticleDOI
Global optimization using interval analysis -- the multi-dimensional case
TL;DR: In this paper, interval analysis is used to compute the global minimum of a function of n variables over ann-dimensional parallelopiped with sides parallel to the coordinate axes, providing infallible bounds on both the globally minimum value of the function and the point(s) at which the minimum occurs.
Proceedings ArticleDOI
Guaranteeing the topology of an implicit surface polygonization for interactive modeling
Barton T. Stander,John Hart +1 more
TL;DR: The impact of this work is a topologically-guaranteed polygonization technique, and the ability to directly and accurately manipulate polygonized implicit surfaces in real time.
Journal ArticleDOI
Bounding solutions of systems of equations using interval analysis
TL;DR: In this article, the interval Newton method was used for bounding solutions to a set of n nonlinear equations, and an improved version was given, which is a superior type of Newton method to Krawczyk's method.
Journal ArticleDOI
Global optimization using interval analysis: The one-dimensional case
TL;DR: In this paper, interval analysis is used to compute the minimum value of a twice continuously differentiable function of one variable over a closed interval, and when both the first and second derivatives of the function have a finite number of isolated zeros, their method never fails to find the global minimum.
References
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On the Newton Method in Interval Analysis
TL;DR: In this paper, an interval type Newton method for vector equations in the n-dimensional Euclidean space is investigated, where the interval is defined as the interval of the interval.