Near-best L1 approximations on circular and elliptical contours |
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Authors: | J C Mason |
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Institution: | Department of Mathematics and Ballistics, Royal Military College of Science, Shrivenham, Swindon, Wiltshire, England |
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Abstract: | Polynomial approximations are obtained to analytic functions on circular and elliptical contours by forming partial sums of order n of their expansions in Taylor series and Chebyshev series of the second kind, respectively. It is proved that the resulting approximations converge in the L1 norm as n → ∞, and that they are near-best L1 approximations within relative distances of the order of log n. Practical implications of the results are discussed, and they are shown to provide a theoretical basis for polynomial approximation methods for the evaluation of indefinite integrals on contours. |
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