Numerical methods and programming
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Num. Meth. Prog.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

Вычислительные методы и приложения

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}


Linking options:
  • http://mi.mathnet.ru/eng/vmp496
  • http://mi.mathnet.ru/eng/vmp/v8/i4/p311

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Numerical methods and programming
    Number of views:
    This page:44
    Full text:16

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2022