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<p>In this paper, we consider a multistep Shanks transformation where the sequences are elements of some associative but non-commutative algebra. It can be expressed by some quasideterminants. We demonstrate that this non-commutative multistep Shanks transformation can be recursively implemented by a non-commutative version of the multistep <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation>-algorithm. Applications of the non-commutative multistep <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation>-algorithm to integrable systems and numerical computation of a partial differential equation and some matrix equations are also presented.</p>

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Applications of quasideterminants to non-commutative multistep \(\varepsilon \)-algorithm

  • 期刊论文

  • 发表日期：

    2025年3月14日

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  • Yi He,
  • Shi-Hao Li,
  • Jian-Qing Sun,
  • Yuan-Zi Wang

摘要

In this paper, we consider a multistep Shanks transformation where the sequences are elements of some associative but non-commutative algebra. It can be expressed by some quasideterminants. We demonstrate that this non-commutative multistep Shanks transformation can be recursively implemented by a non-commutative version of the multistep \(\varepsilon \) ε -algorithm. Applications of the non-commutative multistep \(\varepsilon \) ε -algorithm to integrable systems and numerical computation of a partial differential equation and some matrix equations are also presented.