A geometric consistency theorem for a symbolic perturbation scheme

Chee Keng Yap

doi:10.1016/0022-0000(90)90016-E

A geometric consistency theorem for a symbolic perturbation scheme

Chee Keng Yap

Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

In a previous paper, we introduced a generic solution to the problem of data degeneracy in geometric algorithms. The scheme is simple to use: algorithms qualifying under our requirements just have to use a prescribed blackbox for polynomial evaluation in order to achieve a symbolic perturbation of data. In this paper, we introduce the concept of an infinitesimal perturbation and show that our method is consistent relative to such perturbations.

Original language	English (US)
Pages (from-to)	2-18
Number of pages	17
Journal	Journal of Computer and System Sciences
Volume	40
Issue number	1
DOIs	https://doi.org/10.1016/0022-0000(90)90016-E
State	Published - Feb 1990

ASJC Scopus subject areas

Theoretical Computer Science
Computer Networks and Communications
Computational Theory and Mathematics
Applied Mathematics

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10.1016/0022-0000(90)90016-E

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title = "A geometric consistency theorem for a symbolic perturbation scheme",

abstract = "In a previous paper, we introduced a generic solution to the problem of data degeneracy in geometric algorithms. The scheme is simple to use: algorithms qualifying under our requirements just have to use a prescribed blackbox for polynomial evaluation in order to achieve a symbolic perturbation of data. In this paper, we introduce the concept of an infinitesimal perturbation and show that our method is consistent relative to such perturbations.",

author = "Yap, {Chee Keng}",

note = "Funding Information: *This work was supported by the Deutsche Forschungs Gemeinschaft, SFB 124, TP B2, at the Universitaet des Saarlandes; it is also supported in part by NSF Grants DCR-84-01898 and CCR-8703458.",

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N2 - In a previous paper, we introduced a generic solution to the problem of data degeneracy in geometric algorithms. The scheme is simple to use: algorithms qualifying under our requirements just have to use a prescribed blackbox for polynomial evaluation in order to achieve a symbolic perturbation of data. In this paper, we introduce the concept of an infinitesimal perturbation and show that our method is consistent relative to such perturbations.

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A geometric consistency theorem for a symbolic perturbation scheme

Abstract

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