Journal of Siberian Federal University. Mathematics & Physics / Construction of Interpolation Splines Minimizing the Semi-norm in the Space K2(Pm)

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Journal of Siberian Federal University. Mathematics & Physics: 2018, Vol. 11, Issue 3
Hayotov, Abdullo R.
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Hayotov, Abdullo R.: V.I. Romanovskiy Institute of Mathematics Uzbekistan Academy of Sciences M. Ulugbek street, 81, Tashkent, 100125 Uzbekistan;
interpolation spline; Hilbert space; norm minimizing property; Sobolev’s method; discrete argument function

In ∫ the present paper, using S.L. Sobolev’s method, interpolation splines that minimize the expression 1 0 (φ(m)(x)+!2φ(m�����2)(x))2dx in the space K2(Pm) are constructed. Explicit formulas for the coefficients of the interpolation splines are obtained. The obtained interpolation splines are exact for monomials 1; x; x2; : : : ; xm�����3 and for trigonometric functions sin !x and cos !x.

Paper at repository of SibFU