Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A simplicial mapping method for locating the zeros of a function

Authors: C. S. Hsu and W. H. Zhu
Journal: Quart. Appl. Math. 42 (1984), 41-59
MSC: Primary 65H05
DOI: https://doi.org/10.1090/qam/736504
MathSciNet review: 736504
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Abstract: The currently available methods of finding the zeros of a vector function are quite effective but they do require a prior knowledge of the approximate locations of the zeros. Such a knowledge is, however, often not available, hence making the task of finding the zeros very difficult. Developed in this paper is a method which enables us to search the whole domain of interest in a systematic way to locate all the simple zeros approximately. This method complements naturally the various conventional iteration procedures. The method involves (i) partitioning the domain into a system of simplexes and (ii) at each simplex examining a local simplicial mapping induced by the given function in order to test whether a zero is present. Special properties of the barycentric coordinates are used in devising a simple testing procedure which makes the method viable and effective.

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DOI: https://doi.org/10.1090/qam/736504
Article copyright: © Copyright 1984 American Mathematical Society

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