Approximation to conjugate functions

Fourier Approximation of Functions Conjugate to the Functions Belonging to Weighted Lipschitz Class

The study of error estimates of periodic functions in L(p ≥ 1)-spaces through Fourier series, although is an old problem and known as Fourier approximation in the existing literature, has been of a growing interests over the last four decades. The most common methods used for the determination of the degree of approximation of periodic functions are based on the minimization of the L-norm of f(...

A stochastic conjugate gradient method for the approximation of functions

We consider the best approximation of a function by a linear combination of a set of linearly independent basis functions, for example, by a polynomial of a certain degree. The function to be approximated is not known explicitly, but the input and output of the function can be observed with samples. The input samples are from a random process with a certain probability density function, and its...

Conjugate Approximation Functions in Finite-element Analysis* By

In this paper a theory of conjugate approximations is developed which provides a fundamental basis for most methods of continuous piecewise approximation. It is shown that for a given finite set of base functions used in an approximation there corresponds another set of conjugate functions which play a significant role in approximate methods of analysis. In the case of finite-element approximat...

APPROXIMATION OF 3D-PARAMETRIC FUNCTIONS BY BICUBIC B-SPLINE FUNCTIONS

In this paper we propose a method to approximate a parametric 3 D-function by bicubic B-spline functions

On Padé Approximation of Some Practical Functions