A Simple Procedure for Setting the Efficient Starting Values of the Durand-Kerner Itereation

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Other Title
  • Durand-Kerner法の効率的な初期値の簡単な設定法

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Description

We propose a simple procedure for setting the efficient starting values of the Durand-Kerner iteration, which finds all zeros α_i(i = 1, ・・・, n) of a polynomial of degree n simultaneously. In our new procedure, the starting values are located on the circle centered at β with radius γ_<gm>where β = 1/nΣ^^n__<i=1>α_i, and γ_<gm> is the geometric mean of the deviations |α_i - β|. The computational cost for this procedure is extremely cheap compared with that for Aberth's procedure. Moreover, the various numerical examples show that our new method reduces the number of iterations tremendously over any other ones, particularly when some of the deviations |α_i - β| are large.

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Details 詳細情報について

  • CRID
    1390001205768492928
  • NII Article ID
    110001883564
  • NII Book ID
    AN10367166
  • DOI
    10.11540/jsiamt.3.4_451
  • ISSN
    24240982
  • Text Lang
    ja
  • Data Source
    • JaLC
    • CiNii Articles
  • Abstract License Flag
    Disallowed

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