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Bernstein Fractal Trigonometric Approximation
Acta Applicandae Mathematicae, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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An Interpolatory Rational Trigonometric Approximation
SIAM Journal on Numerical Analysis, 1981In this paper we introduce a sequence of positive linear, interpolating operators $\Lambda _n (n = 1,2, \cdots )$, which map $c_{2\pi } $ (class of continuous ${2\pi }$-periodic functions) into the set of rational trigonometric functions of order $ \leqq 2n - 2$. Moreover, they satisfy \[ \left| {f(x) - \Lambda _n (f,x)} \right| \leqq 2\omega _f \left(
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Approximation by local trigonometric splines
Mathematical Notes, 2005Let \(W_\alpha\), \(\alpha>0\), be the class of 1-periodic functions \(f: {\mathbb R} \to {\mathbb R}\) having a locally absolutely continuous derivative \(f'\) for which \(\| f''+\alpha^2 f \| _{L_\infty [0,1]} \leq 1\). The authors consider approximation of \(W_\alpha\) by the space of 1-periodic trigonometric splines representable on each interval \(
Kostousov, K. V., Shevaldin, V. T.
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Trigonometric approximation of functions in $$L_1$$-norm
Periodica Mathematica Hungarica, 2021The \(L_1\)-approximation of the functions \(f \in {\operatorname{Lip}}(\alpha,1 ...
Chandra, Prem, Karanjgaokar, Varsha
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Some inequalities in trigonometric approximation
Bulletin of the Australian Mathematical Society, 1973For a nonconstant L2 (−π, π) function f, we prove that and that the inequalities are sharp.
Ching, Chin-Hung, Chui, Charles K.
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Trigonometric Approximations for Bessel Functions
IEEE Transactions on Aerospace and Electronic Systems, 1986Bessel functions, used extensively in mathematical physics, electromagnetics, and communication-system theory, must often be approximated by appropriate formulas. The functions J?(x) and I?(x) for integer values of p are well approximated by the sum of a small number of circular and hyperbolic sines or cosines, respectively, when x is not too large, e ...
Nelson M. Blachman +1 more
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Approximation of trigonometric functions by trigonometric polynomials with interpolation
Journal of Contemporary Mathematical Analysis, 2010The paper studies the approximation order of periodic functions by trigonometric polynomials with interpolation in arbitrary set of nodes. A method of construction of Hermite interpolation polynomials is pointed out.
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FRACTAL TRIGONOMETRIC POLYNOMIALS FOR RESTRICTED RANGE APPROXIMATION
Fractals, 2016One-sided approximation tackles the problem of approximation of a prescribed function by simple traditional functions such as polynomials or trigonometric functions that lie completely above or below it. In this paper, we use the concept of fractal interpolation function (FIF), precisely of fractal trigonometric polynomials, to construct one-sided ...
Chand, A. K. B. +3 more
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Trigonometric background multivariate smooth trigonometric singular integrals approximations
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. MatemáticaszbMATH Open Web Interface contents unavailable due to conflicting licenses.
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APPROXIMATE POLYNOMIALS OF TRIGONOMETRICAL SERIES
Survey Review, 1973AbstractApproximate polynomials of the arctangent, tangent, cosine and sine series are offered which are suitable for use on small desk-top programmable computers, or on pocket computers in the field, which do not have inbuilt facilities for evaluating trigonometrical functions.
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