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<p>Using recently developed algorithms, we compute and compare best <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(L^\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>∞</mi> </msup> </math></EquationSource> </InlineEquation> rational approximations of analytic functions on the unit disk. Although there is some theory for these problems going back decades, this may be the first computational study. To compute the <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> best approximations, we employ a new formulation of TF-IRKA in barycentric form.</p>

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\(L^2\) and \(L^\infty \) rational approximation on the unit disk

  • 期刊论文

  • 发表日期：

    2026年8月1日

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  • Michael S. Ackermann,
  • Sean Reiter,
  • Lloyd N. Trefethen

摘要

Using recently developed algorithms, we compute and compare best \(L^2\) L 2 and \(L^\infty \) L ∞ rational approximations of analytic functions on the unit disk. Although there is some theory for these problems going back decades, this may be the first computational study. To compute the \(L^2\) L 2 best approximations, we employ a new formulation of TF-IRKA in barycentric form.