0. Introduction. It is the purpose of this note to show that the several minimum properties of odd degree polynomial spline functions [4, 18] all derive from the fact that spline functions are representers of appropriate bounded linear functionals in an appropriate Hilbert space. (These results were first announced in Notices, Amer. Math. Soc., 11 (1964) 681.) In particular, spline interpolatio...

In this paper a new architecture for multichannel blind deconvolution in the frequency domain is presented. It is based on a new complex-domain non-linear function, built with a couple of spline functions, one for the real and one for the imaginary part, whose control points are adaptively changed using gradient-based techniques. B-spline functions are used since they allow to impose only simpl...

This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel B-splines are introduced to compute a C 2 -continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarse-tofine hierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desired interpolation function. Large p...

Image encryption is one of most useful way of securing image data. Traditional data security algorithms are also used over images but due to the bulkiness of image data they are not useful. Chaotic sequences play a very good role in image cryptographic system, due to their high sensitivity to initial condition and other properties. In this paper, B-spline functions of first three orders are stu...

A diierential equation of the form Dp(x)Du(x) = f(x; u(x)) is solved by collocation, using a class of spline functions of order 3. A restriction of each spline function to any subinterval of the partition is piecewisely in the kernel of the operator DDp(x)D. A coeecient p(x) may be singular. An algorithm is described by means of which a B-spline basis could be eeciently constructed. Some numeri...