Interpolation with minimal value of $L_{2}$-norm of linear differential operator for finite collections of data

Sergey I. Novikov

0009-0002-5945-7614

Scopus Author ID: 16421932500

Researcher ID: 9780

1. Krasovskii Institute of Mathematics and Mechanics the Ural Branch of Russian Academy of Sciences, Yekaterinburg, Russia

Sergey.Novikov@imm.uran.ru

An exact solution is found to the problem of interpolation on an arbitrary finite interval $[a, b]$ with the smallest $L_{2}$-norm of the linear differential operator for finite collections of data from the unit ball of the space $l_{2}^{N}$. Interpolation is performed at knots of an arbitrary fixed $N$-point grid \linebreak$\Delta_{N}:\ x_{1}

УДК 517.5

Keywords: interpolation, ${\cal L}$-spline, Favard type interpolation problem, dis\-conjugacy, linear differential operator, the Green function, reproducing kernel.