Algorithm 13. Approximate function expansion into a Chebyshev series
Z. Cylkowski (1971)
Applicationes Mathematicae
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Z. Cylkowski (1971)
Applicationes Mathematicae
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S. Lewanowicz (1976)
Applicationes Mathematicae
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Anna Trzmielak (1977)
Applicationes Mathematicae
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Frank William John Olver (1968)
Aplikace matematiky
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Roberto Barrio (1998)
Extracta Mathematicae
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G. Mühlbach (1978/79)
Numerische Mathematik
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Roberto Barrio, Antonio Elipe (2002)
Revista Matemática Complutense
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In this paper, we present the simple and double compression algorithms with an error control for compressing satellite data corresponding to several revolutions. The compressions are performed by means of approximations in the norm L by finite series of Chebyshev polynomials, with their known properties of fast evaluation, uniform distribution of the error, and validity over large intervals of time. By using the error control here introduced, the number of terms of the series is given...
Krystyna Ziętak (1988)
Applicationes Mathematicae
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Grigori Litvinov (2003)
Open Mathematics
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The error autocorrection effect means that in a calculation all the intermediate errors compensate each other, so the final result is much more accurate than the intermediate results. In this case standard interval estimates (in the framework of interval analysis including the so-called a posteriori interval analysis of Yu. Matijasevich) are too pessimistic. We shall discuss a very strong form of the effect which appears in rational approximations to functions. The error autocorrection...
Hoai An Le Thi, Mohand Ouanes (2006)
RAIRO - Operations Research
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The purpose of this paper is to demonstrate that, for globally minimize one dimensional nonconvex problems with both twice differentiable function and constraint, we can propose an efficient algorithm based on Branch and Bound techniques. The method is first displayed in the simple case with an interval constraint. The extension is displayed afterwards to the general case with an additional nonconvex twice differentiable constraint. A quadratic bounding function which is better than...