General Degree of Periodic Spline Functions

General Degree of Periodic Spline Functions

In this paper we consider spline function of general degree m which has the same area as the function does in each partition of the sub-intervals. The existence and uniqueness in general of spline functions also been studied and obtained the result. : In this paper we consider spline function of general degree, i.e.,of degree m, m=2,3,.... We first give definitions and notations. We take 0 =x 0...

Learnability of periodic activation functions: General results

On-line learning in the presence of continuous periodic activation functions is studied analytically. The effect of the ambiguity ~an infinite number of inputs with different local fields can produce the same output! on the learnability is examined. A universal interplay between the general features of the activation function ~wave number, parity, etc.! and the critical learning rate is found. ...

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

INTERPOLATION BY HYPERBOLIC B-SPLINE FUNCTIONS

In this paper we present a new kind of B-splines, called hyperbolic B-splines generated over the space spanned by hyperbolic functions and we use it to interpolate an arbitrary function on a set of points. Numerical tests for illustrating hyperbolic B-spline are presented.

Smoothing by Spline Functions