Construction of interpolation splines minimizing the semi-norm in the space $K_2(P_m)$

Abstract

In the present paper, using S.L. Sobolev's method, interpolation spline that minimizes the expression ${\int }_0^1({\phi }^{(m)}(x)+{\omega }^2{\phi }^{(m-2)}(x){)}^{2}dx$ in the $K_2(P_m)$ space are constructed. Explicit formulas for the coefficients of the interpolation splines are obtained. The obtained interpolation spline is exact for monomials $1,x,x^2,...,x^{m-3}$ and for trigonometric functions $\sin \omega x$ and $\cos \omega x$.

References in corpus (1)

• Optimal quadrature formulas of closed type in the space $L_2^{(m)}(0,1)$