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- W2097807715 abstract "We present a new set oriented numerical method for the detection of all the zeros of a given (smooth) function g : Rn → Rn within a compact region. The underlying idea is to view classical iteration schemes as specific dynamical systems and to apply adaptive multilevel subdivision techniques for the computation of their fixed points. These techniques have previously been developed for the identification of arbitrary invariant sets of dynamical systems. Based on this idea we construct a subdivision algorithm which allows us to create close coverings of the set of zeros of g. We prove convergence of this algorithm in a general abstract context and propose three different realizations which are motivated by the theoretical results. Finally, we discuss the numerical efficiency of these algorithms by a comparison with a standard zero finding procedure using a routine from the NAG library." @default.
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- W2097807715 date "2002-04-01" @default.
- W2097807715 modified "2023-09-23" @default.
- W2097807715 title "Finding zeros by multilevel subdivision techniques" @default.
- W2097807715 doi "https://doi.org/10.1093/imanum/22.2.167" @default.
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