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- W4300533772 abstract "We describe an expansion of Legendre polynomials, analogous to the Taylor expansion, to approximate arbitrary functions. We show that the polynomial coefficients in Legendre expansion, therefore the whole series, converge to zero much more rapidly compared to the Taylor expansion of the same order. Furthermore, using numerical analysis using sixth-order polynomial expansion, we demonstrate that the Legendre polynomial approximation yields an error at least an order of magnitude smaller than the analogous Taylor series approximation. This strongly suggests that Legendre expansions, instead of Taylor expansions, should be used when global accuracy is important." @default.
- W4300533772 created "2022-10-03" @default.
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- W4300533772 date "2011-08-02" @default.
- W4300533772 modified "2023-09-24" @default.
- W4300533772 title "A Polynomial Approximation for Arbitrary Functions" @default.
- W4300533772 doi "https://doi.org/10.48550/arxiv.1108.0608" @default.
- W4300533772 hasPublicationYear "2011" @default.
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