Nonperiodic Trigonometric Polynomial Approximation
نویسندگان
چکیده
منابع مشابه
Nonperiodic Trigonometric Polynomial Approximation
The most common approach for approximating non-periodic function defined on a finite interval is based on considering polynomials as basis functions. In this paper we will address the non-optimallity of polynomial approximation and suggest to switch from powers of x to powers of sin(px) where p is a parameter which depends on the dimension of the approximating subspace. The new set does not suf...
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Abstract. The classical Gibbs phenomenon for the Fourier sections (best L2trigonometric polynomial approximants) of a jump function asserts that, near the jump, the~e sections "overshoot" the function by an asymptotically constant factor g (the L2-Gibbs constant). In this paper we show that, for a class of one-jump discontinuous functions, a similar phenomenon holds for the trigonometric polyno...
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for some nonnegative integer k and complex numbers a0, . . . , ak, b1, . . . , bk ∈ C. Trigonometric polynomials and their series counterparts, the Fourier series, play an important role in many areas of pure and applied mathematics and are likely to be quite familiar to the reader. When reflecting on the terminology, however, it is reasonable to wonder why the term trigonometric polynomial is ...
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A symmetric basis of trigonometric polynomial space is presented. Based on the basis, symmetric trigonometric polynomial approximants like Bernstein polynomials are constructed. Two kinds of nodes are given to show that the trigonometric polynomial sequence is uniformly convergent. The convergence of the derivative of the trigonometric polynomials is shown. Trigonometric quasi-interpolants of r...
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These notes are prepared as lecture notes exclusively for the participants of this conference only. Any reproduction in any media, or any use for any other purpose of any part of this manuscript, without an expressed written consent of the author is unlawful.thorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conc...
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ژورنال
عنوان ژورنال: Journal of Scientific Computing
سال: 2013
ISSN: 0885-7474,1573-7691
DOI: 10.1007/s10915-013-9797-6