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A modification of the numerical integration error method for the zero-finding problem of an analytic function

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Abstract

The numerical integration error method (NIEM) is a zero-finding method which is based on the numerical evaluation of integrals of ƒ′/ƒ NIEM is an iterative method of higher-order, and (therefore) a lot of computational complexities are required. Besides it is necessary to select one from a number of choices of NIEM correction. In this paper we introduce an algorithm that improves computational efficiency of NIEM, yielding better results for the case of multiple or clustered zeros. Some numerical examples demonstrating the efficiency of this algorithm are introduced.

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Authors and Affiliations

  1. Interdisciplinary Graduate School of Medicine and Engineering, University of Yamanashi, 400-8511, Kofu, Japan

    Tomohiro Suzuki

  2. Faculty of Education and Human Sciences, University of Yamanashi, 400-8510, Kofu, Japan

    Toshio Suzuki

Authors
  1. Tomohiro Suzuki
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  2. Toshio Suzuki
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Correspondence to Tomohiro Suzuki.

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Suzuki, T., Suzuki, T. A modification of the numerical integration error method for the zero-finding problem of an analytic function. Japan J. Indust. Appl. Math. 22, 353–365 (2005). https://doi.org/10.1007/BF03167489

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  • DOI: https://doi.org/10.1007/BF03167489

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