منابع مشابه
Rational Interpolation at Chebyshev points
The Lanczos method and its variants can be used to solve eeciently the rational interpolation problem. In this paper we present a suitable fast modiication of a general look-ahed version of the Lanczos process in order to deal with polynomials expressed in the Chebyshev orthogonal basis. The proposed approach is particularly suited for rational interpolation at Chebyshev points, that is, at the...
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Let T be a Jordan curve in the complex plane, and let Í) be the compact set bounded by T. Let / denote a function analytic on O. We consider the approximation of / on fî by a polynomial p of degree less than n that interpolates / in n points on T. A convenient way to compute such a polynomial is provided by the Newton interpolation formula. This formula allows the addition of one interpolation ...
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This paper improves error bounds for Gauss, Clenshaw-Curtis and Fejér’s first quadrature by using new error estimates for polynomial interpolation in Chebyshev points. We also derive convergence rates of Chebyshev interpolation polynomials of the first and second kind for numerical evaluation of highly oscillatory integrals. Preliminary numerical results show that the improved error bounds are ...
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We examine to what extent finite-dimensional spaces defined on locally compact subsets of the line and possessing various weak Chebyshev properties (involving sign changes, zeros, alternation of best approximations, and peak points) can be uniformly approximated by a sequence of spaces having related properties. r 2003 Elsevier Science (USA). All rights reserved.
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Stable polynomial evaluation and interpolation at n Chebyshev or adjusted (expanded) Chebyshev points is performed using O(nlog’ n) arithmetic operations, to be compared with customary algorithms either using on the order of n* operations or being unstable. We also evaluate a polynomial of degree d at the sets of n Chebyshev or adjusted (expanded) Chebyshev points using O(dlog d log n) if n 5 d...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1973
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1973-0370365-6