Construction of the sixth order algebraic-hyperbolic interpolation natural spline
Keywords:
parametric interpolation spline, Hilbert space, Sobolev’s method, discrete argument function, discrete analogy of the differential operatorAbstract
Now splines are being constructed in different spaces and with different methods, and their application is widely studied. In this work, We construct a parametric spline that belongs ????3,???? space. For this , we will use the Sobolev method and obtain a spline function for the approximate calculation of the unknown function. Firstly, we will present the interpolation spline function under which conditions gives a minimum to the norm in a certain Hilbert space. We will give a equations system to find the coefficints of interpolation natural spline spline. We use Sobolev method to find the coefficients of this spline. This method allows to obtain an analytical solution of such systems. This method is based on constructing a discrete analogue of the differential operator ????*????. When we found the coefficients of the sixth order algebraic-hyperbolic interpolation natural siline, we obtain the exact expression of this spline.
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