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<p>Given a multivariate polynomial <i>f</i>, we consider an approximate decomposition in the Hamming distance, that is, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({f}{=} {g} {\circ } {h} \,{+ \, \delta },\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo>=</mo> <mi>g</mi> <mo>∘</mo> <mi>h</mi> <mspace width="0.166667em" /> <mrow> <mo>+</mo> <mspace width="0.166667em" /> <mi>δ</mi> </mrow> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> where <i>g</i> is a univariate polynomial, <i>h</i> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\delta }\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation> are multivariate polynomials, and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\delta }\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation> has few terms. We propose an algorithm for computing an approximate decomposition and introduce its application to multivariate Horner’s scheme.</p>

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An Approximate Decomposition of a Multivariate Polynomial and Its Application

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月7日

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  • Rikuna Tokuda,
  • Hiroshi Sekigawa

摘要

Given a multivariate polynomial f, we consider an approximate decomposition in the Hamming distance, that is, \({f}{=} {g} {\circ } {h} \,{+ \, \delta },\) f = g ∘ h + δ , where g is a univariate polynomial, h and \({\delta }\) δ are multivariate polynomials, and \({\delta }\) δ has few terms. We propose an algorithm for computing an approximate decomposition and introduce its application to multivariate Horner’s scheme.