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

Abdullo R. Hayotov

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

Numerical Analysis 2014-10-21 v1

Authors: Abdullo R. Hayotov

Abstract

In the present paper, using S.L. Sobolev's method, interpolation spline that minimizes the expression $\int_0^1(\varphi^{(m)}(x)+\omega^2\varphi^{(m-2)}(x))^2dx$ 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 $\cos\omega x$ .

Keywords

interpolation splines Sobolev method semi-norm minimization $K_2(P_m)$ space explicit formulas trigonometric functions

Cite

@article{arxiv.1410.5312,
  title  = {Construction of interpolation splines minimizing the semi-norm in the space $K_2(P_m)$},
  author = {Abdullo R. Hayotov},
  journal= {arXiv preprint arXiv:1410.5312},
  year   = {2014}
}

Related papers

View all related →