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Obtaining a banded system of equations in complete spline interpolation problem via B-spline basis

100%

Volkov Y.

tom 10

nr 1

352-356

We study the problem of interpolation by a complete spline of 2n − 1 degree given in B-spline representation. Explicit formulas for the first nand the last ncoefficients of B-spline decomposition are found. It is shown that other B-spline coefficients can be computed as a solution of a banded system of an equitype linear equations.

Application of non-uniform B-Splines of 2-nd order for description vertical distribution of sound speed in water

100%

Makar A.

tom Vol. 12

133-140

Modeling of the vertical distribution of the sound speed in water is useful during determination of the depth on the basis of the acoustic method, modeling refraction phenomena and determination the trajectory of the acoustic wave. For modeling 1D functions (vertical distribution of the sound speed) and 2D (surface of the sea bottom for hydrography) uniform B-Splines was used. In this paper description of uniform B-Splines and description and application of non-uniform B-Splines have been presented.