نتایج جستجو برای: trigonometric function

تعداد نتایج: 1216172  

2002
Dimitar K. Dimitrov

There are various reasons for the interest in the problem of constructing nonnegative trigonometric polynomials. Among them are: Cesàro means and Gibbs’ phenomenon of the the Fourier series, approximation theory, univalent functions and polynomials, positive Jacobi polynomial sums, orthogonal polynomials on the unit circle, zero-free regions for the Riemann zeta-function, just to mention a few....

Journal: :CoRR 2013
Ágoston Róth Imre Juhász Alexandru Kristály

We construct a constrained trivariate extension of the univariate normalized B-basis of the vector space of trigonometric polynomials of arbitrary (finite) order n ∈ N defined on any compact interval [0, α], where α ∈ (0, π). Our triangular extension is a normalized linearly independent constrained trivariate trigonometric function system of dimension δn = 3n (n+ 1) + 1 that spans the same vect...

2010
Gwang Hui Kim Yeol Je Cho

We will investigate the superstability of the hyperbolic trigonometric functional equation from the following functional equations: fx y ± gx − y λfxgy andfx y ± gx − y λgxfy, which can be considered the mixed functional equations of the sine function and cosine function, the hyperbolic sine function and hyperbolic cosine function, and the exponential functions, respectively.

Journal: :SIAM J. Scientific Computing 2000
Thomas Strohmer

Abstract. Trigonometric polynomials are widely used for the approximation of a smooth function f from a set of nonuniformly spaced samples {f(xj )} N−1 j=0 . 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. Using the polynomial degree as regularization parameter we d...

A.S Sayyad Y.M Ghugal,

In this paper a variationally consistent trigonometric shear deformation theory is presented for the free vibration of thick isotropic square and rectangular plate. In this displacement based theory, the in-plane displacement field uses sinusoidal function in terms of thickness coordinate to include the shear deformation effect. The cosine function in terms of thickness coordinate is used in tr...

Abdellah Lamnii Jaoud Dabounou Omar El Khayyari

By using the trigonometric uniform splines of order 3 with a real tension factor, a numericalmethod is developed for solving a linear second order boundary value problems (2VBP) withDirichlet, Neumann and Cauchy types boundary conditions. The moment at the knots isapproximated by central finite-difference method. The order of convergence of the methodand the theory is illustrated by solving tes...

2006
O. L. VINOGRADOV

In this paper, a new method is introduced for the proof of sharp Jacksontype inequalities for approximation of convolution classes of functions defined on the real line. These classes are approximated by linear operators with values in sets of entire functions of exponential type. In particular, a sharp Jackson-type inequality for the even-order derivatives of the conjugate function is proved. ...

1996
HEIKE FAßBENDER Heike Faßbender

Recently fast, efficient and reliable algorithms for discrete least-squares approximation of a real-valued function given at arbitrary distinct nodes in [0, 2π) by trigonometric polynomials were presented in different papers. These algorithms are based on schemes for the solution of inverse unitary eigenproblems and require only O(mn) arithmetic operations as compared to O(mn) operations needed...

Journal: :Statistica Sinica 2024

We introduce nonparametric tests of independence for bivariate circular data based on trigonometric moments. Our contributions lie in (i) proposing that are locally and asymptotically optimal against cosine von Mises alternatives (ii) extending these tests, via the empirical characteristic function, to obtain consistent broader sets alternatives, eventually being omnibus. thus provide a collect...

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