NDLI: Chebyshev interpolation polynomial-based tools for rigorous computing

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Chebyshev interpolation polynomial-based tools for rigorous computing

Content Provider	ACM Digital Library
Author	Joldeş, Mioara Brisebarre, Nicolas
Abstract	Performing numerical computations, yet being able to provide rigorous mathematical statements about the obtained result, is required in many domains like global optimization, ODE solving or integration. Taylor models, which associate to a function a pair made of a Taylor approximation polynomial and a rigorous remainder bound, are a widely used rigorous computation tool. This approach benefits from the advantages of numerical methods, but also gives the ability to make reliable statements about the approximated function. Despite the fact that approximation polynomials based on interpolation at Chebyshev nodes offer a quasi-optimal approximation to a function, together with several other useful features, an analogous to Taylor models, based on such polynomials, has not been yet well-established in the field of validated numerics. This paper presents a preliminary work for obtaining such interpolation polynomials together with validated interval bounds for approximating univariate functions. We propose two methods that make practical the use of this: one is based on a representation in Newton basis and the other uses Chebyshev polynomial basis. We compare the quality of the obtained remainders and the performance of the approaches to the ones provided by Taylor models.
Starting Page	147
Ending Page	154
Page Count	8
File Format	PDF
ISBN	9781450301503
DOI	10.1145/1837934.1837966
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2010-07-25
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Rigorous computing Taylor models Interpolation polynomial Chebyshev polynomials Validated numerics
Content Type	Text
Resource Type	Article

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