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<p>It is shown that Thiele’s interpolation continued fraction has either 2<i>k -</i> 1 approximants if a function is a <i>k</i> th degree polynomial or 2<i>k</i> approximants for the function <i>g</i>(<i>z</i>) = <i>a</i>/(<i>z - α</i>)<sup><i>k</i></sup><i>.</i> We specify the conditions under which the coefficients of the continued fraction are finite and nonzero. For a given set of values of functions at the nodes, we propose an algorithm that either constructs a nondegenerate interpolation continued fraction or proves the impossibility of this construction. We also present some examples.</p>

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A Nondegenerate Interpolation Continued Fraction

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • Yuliia Myslo,
  • Mykhailo Pahirya

摘要

It is shown that Thiele’s interpolation continued fraction has either 2k - 1 approximants if a function is a k th degree polynomial or 2k approximants for the function g(z) = a/(z - α)k. We specify the conditions under which the coefficients of the continued fraction are finite and nonzero. For a given set of values of functions at the nodes, we propose an algorithm that either constructs a nondegenerate interpolation continued fraction or proves the impossibility of this construction. We also present some examples.