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- W3037281419 abstract "In approximation theory, it is standard to approximate functions by polynomials expressed in the Chebyshev basis. Evaluating a polynomial $f$ of degree n given in the Chebyshev basis can be done in $O(n)$ arithmetic operations using the Clenshaw algorithm. Unfortunately, the evaluation of $f$ on an interval $I$ using the Clenshaw algorithm with interval arithmetic returns an interval of width exponential in $n$. We describe a variant of the Clenshaw algorithm based on ball arithmetic that returns an interval of width quadratic in $n$ for an interval of small enough width. As an application, our variant of the Clenshaw algorithm can be used to design an efficient root finding algorithm." @default.
- W3037281419 created "2020-07-02" @default.
- W3037281419 creator A5028023163 @default.
- W3037281419 creator A5056802862 @default.
- W3037281419 date "2019-12-12" @default.
- W3037281419 modified "2023-10-16" @default.
- W3037281419 title "Evaluation of Chebyshev polynomials on intervals and application to root finding" @default.
- W3037281419 doi "https://doi.org/10.48550/arxiv.1912.05843" @default.
- W3037281419 hasPublicationYear "2019" @default.
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