Locating Safe Starting Regions for Iterative Methods: A Heuristic Algorithm

Jones, S. T.

doi:10.1016/b978-0-12-518850-0.50030-5

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1985

1986

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Cited by 3 publications

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“…This is obviously important when performing Newton iteration. The scheme (3.3) is referred to as interval Newton iteration and has been discussed in great detail by Moore [11], [13], Wolfe [20], Krawczyk [7], and Jones [6], to name a few. In these works it has been shown that (3.3) will converge under the same conditions as theorem 3.2.…”

Section: Theoremmentioning

confidence: 99%

On ray tracing parametric surfaces

Toth

1985

Proceedings of the 12th Annual Conference on Computer Graphics and Interactive Techniques - SIGGRAPH '85

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A new method for ray tracing parametric surfaces is presented. The new algorithm solves the ray surface intersection directly using multivariate Newton iteration. This provides enough generality to render surfaces which could not be ray traced using existing methods. To overcome the problem of finding a starting point for the Newton algorithm, techniques from Interval Analysis are employed. The results are presented in terms of solving a general nonlinear system of equations f(x) = 0, and thus can be extended to a large class of problems which arise in computer graphics. General Terms: Algorithms

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Section: Theoremmentioning

confidence: 99%