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Some Approximations for Trigonometrical Functions
1980It is shown that better approximations of tan(x) are obtained if the singular part is taken out, i.e. if we write tan(x) = S(x) + R(x) where S contains the singular part of tan in the sense that the rest R(x) is finite for x → one or several of the points ±π/2,±3π/2,...
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Abstract Fractional Trigonometric Korovkin Approximation
2017In this chapter we study quantitatively with rates the trigonometric fractional convergence of sequences of linear operators applied on Banach space valued functions.
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Greedy Algorithm and m -Term Trigonometric Approximation
Constructive Approximation, 1998This paper is devoted to the nonlinear method of approximation of the following type. For the periodic function \(f\) it is taken as an approximant a trigonometric polynomial of the form \( G_m(f):= \sum_{k\in \Lambda} \widehat f (k) \exp{i(k,x)}\), where \(\Lambda\subset \mathbf Z^d\) is a set of cardinality \(m\) containing the indices of the \(m ...
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Some Notes on Trigonometric Approximation
2011Let us denote by (c[a, b] c[0, 2p]) the space of all real continuous (2p-periodic) functions f provided with the uniform norm \({\parallel{f}\parallel} = {\mathop{\sup}\limits_{x\in[a,b]}}\,|\,f(x)\,|\,\,\,{\left(=\,\,{\mathop{\sup}\limits_{x\in[a,b]}}\,|\,f(x)\,|\right)}.\)
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Sharp Exponential Approximate Inequalities for Trigonometric Functions
Results in Mathematics, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Simultaneous Trigonometric Approximation
Journal of Mathematics and Physics, 1952Steinberg, R., Redheffer, R. M.
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APPROXIMATION TO π BY TRIGONOMETRICAL SURDS
The Quarterly Journal of Mathematics, 1953openaire +2 more sources