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 Num. Meth. Prog., 2007, Volume 8, Issue 4, Pages 311–316 (Mi vmp496)

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Computing first-order zeros of analytic functions with large values of derivatives

V. V. Protopopov

Samsung Electronics Co., Ltd.

Abstract: There are some practically important types of complex analytic functions whose zeros are narrowly surrounded by large function values. Zeros of this kind are said to be deep. Computation of deep zeros presents difficulty for commonly used methods because of large values of function derivatives. An efficient algorithm for computing deep zeros is proposed on the basis of contour integration of the function argument.. Its variations along the contour are much smaller than variations of the function values, which makes the algorithm efficient. The location of the argument maxima along the contour of integration yields an initial approximation for the zero whose value is further refined by applying the Muller algorithm.

Keywords: analytic functions, zeros of functions, contour integration, function of complex variable.

Full text: PDF file (148 kB)
UDC: 519.6

Citation: V. V. Protopopov, “Computing first-order zeros of analytic functions with large values of derivatives”, Num. Meth. Prog., 8:4 (2007), 311–316

Citation in format AMSBIB
\Bibitem{Pro07} \by V.~V.~Protopopov \paper Computing first-order zeros of analytic functions with large values of derivatives \jour Num. Meth. Prog. \yr 2007 \vol 8 \issue 4 \pages 311--316 \mathnet{http://mi.mathnet.ru/vmp496}