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On approximation of continuous functions by trigonometric polynomials

Journal of Approximation Theory, 2011
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Hans-Peter Blatt, Vladimir V Andrievskii   +1 more
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Trigonometric approximation of functions in $$L_1$$-norm

Periodica Mathematica Hungarica, 2021
The \(L_1\)-approximation of the functions \(f \in {\operatorname{Lip}}(\alpha,1 ...
Prem Chandra, Varsha Karanjgaokar
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Bernstein Fractal Trigonometric Approximation

Acta Applicandae Mathematicae, 2018
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Vijender Nallapu
exaly   +3 more sources

Trigonometric polynomial approximation in theL 1-norm

Mathematische Zeitschrift, 1979
Franz Peherstorfer
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Monotone Trigonometric Approximation

Mediterranean Journal of Mathematics, 2014
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Leviatan, D., Sidon, J.
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Interpolation and L1-approximation by trigonometric polynomials and blending functions [PDF]

Journal of Approximation Theory, 2012
We present results on interpolation and L1-approximation of periodic functions by trigonometric polynomials and trigonometric blending functions. In Section 1, we obtain an error-representation formula for Hermite–Lagrange interpolation by trigonometric ...
Petrov, P., Dryanov, D.
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A Levinson--Galerkin Algorithm for Regularized Trigonometric Approximation [PDF]

SIAM Journal of Scientific Computing, 2000
Trigonometric polynomials are widely used for the approximation of a smooth function $f$ from a set of nonuniformly spaced samples $\{f(x_j)\}_{j=0}^{N-1}$. If the samples are perturbed by noise, controlling the smoothness of the trigonometric approximation becomes an essential issue to avoid overfitting and underfitting of the data.
Thomas Strohmer
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Approximation by local trigonometric splines

Mathematical Notes, 2005
Let \(W_\alpha\), \(\alpha>0\), 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 \(
Valerii T Shevaldin
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An Interpolatory Rational Trigonometric Approximation

SIAM Journal on Numerical Analysis, 1981
In 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 of trigonometric functions by trigonometric polynomials with interpolation

Journal of Contemporary Mathematical Analysis, 2010
The 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.
exaly   +2 more sources