In the classical theory of cubic interpolation splines there exists an algorithm which works with only On arithmetic operations. Also, smoothing may be computed via Reinsch reduces their computation to and also performs this paper it is shown that many features polynomial spline setting carry over larger class L-splines where L a linear differential operator order 4 constant coefficients. Crite...

the polynomial interpolation in one dimensional space r is an important method to approximate the functions. the lagrange and newton methods are two well known types of interpolations. in this work, we describe the semi inherited interpolation for approximating the values of a function. in this case, the interpolation matrix has the semi inherited lu factorization.

Interpolation and gridding of data are procedures in the physical sciences and are accomplished typically using an averaging or finite difference scheme on an equidistant grid. Cubic splines are popular because of their smooth appearances: however, these functions can have undesirable oscillations between data points. Adding tension to the spline overcomes this deficiency. Here, we derive a tec...

The problem of semi-cardinal spline interpolation was solved by Schoenberg exploiting the piecewise polynomial form of the splines. In the present paper, we propose a new construction for the Lagrange functions of semi-cardinal spline interpolation , based on a radial basis and Fourier transform approach. This approach suggests a way of extending semi-cardinal interpolation to polyharmonic spli...

The paper deals with Div-Curl approximation problem by weighted thin plate splines. The weighted thin plate splines are an extension of the well known thin plate splines and are radial basis functions which allow the approximation and interpolation of a scalar functions from a given scattered data. We show how the weighted thin plate splines may also be used for the approximation and interpolat...

Data measuring and further processing is the fundamental activity in all branches of science technology. interpolation has been an important part computational mathematics for a long time. In paper, we are concerned with by polyharmonic splines arbitrary dimension. We show connection this radial basis functions smooth generating functions, which provide means minimizing L2 norm chosen derivativ...