Rational approximation to trigonometric operators

Approximation by Rational Operators in L Spaces

Monotone Rational Trigonometric Interpolation

This study is concerned with the visualization of monotone data using a piecewise C rational trigonometric interpolating scheme. Four positive shape parameters are incorporated in the structure of rational trigonometric spline. Conditions on two of these parameters are derived to attain the monotonicity of monotone data and other two are left free. Figures are used widely to exhibit that the pr...

Trigonometric rational wavelet bases

We propose a construction of periodic rational bases of wavelets First we explain why this problem is not trivial Construction of wavelet basis is not possible neither for the case of alge braic polynomials nor for the case of rational algebraic functions Of course algebraic polynomials do not belong to L R Nevertheless they can belong to the closure of L R in topology of the generalized conver...

Approximation By Trigonometric Polynomials

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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...