RationalFunctionApproximation.jl: Rational Approximation On Discrete and Continuous Domains
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912752428122112 |
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| author | Driscoll, Tobin A. |
| author_facet | Driscoll, Tobin A. |
| contents | Unlike polynomials, rational functions can represent functions having poles or branch cuts with root-exponential convergence and no Runge phenomenon. Recent developments of the AAA and greedy Thiele algorithms have sparked renewed interest in computational rational approximation. The \textsf{RationalFunctionApproximation} package supplies the fastest known implementations of these methods and the only arbitrary-precision ones. Combined with the \textsf{ComplexRegions} package, it can produce compact and accurate representations of a huge variety of functions over intervals, circles, or other domains in the complex plane. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_06140 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | RationalFunctionApproximation.jl: Rational Approximation On Discrete and Continuous Domains Driscoll, Tobin A. Numerical Analysis Complex Variables 65D15 Unlike polynomials, rational functions can represent functions having poles or branch cuts with root-exponential convergence and no Runge phenomenon. Recent developments of the AAA and greedy Thiele algorithms have sparked renewed interest in computational rational approximation. The \textsf{RationalFunctionApproximation} package supplies the fastest known implementations of these methods and the only arbitrary-precision ones. Combined with the \textsf{ComplexRegions} package, it can produce compact and accurate representations of a huge variety of functions over intervals, circles, or other domains in the complex plane. |
| title | RationalFunctionApproximation.jl: Rational Approximation On Discrete and Continuous Domains |
| topic | Numerical Analysis Complex Variables 65D15 |
| url | https://arxiv.org/abs/2512.06140 |