The extremal function of interpolation formulas in W2(2,0)  space

Abstract

One of the main problems of computational mathematics is the optimization of computational methods in functional spaces. Optimization of computational methods are well demonstrated in the problems of the theory of interpolation formulas. In this paper, we study the problem of constructing an optimal interpolation formula in a Hilbert space. Here, using the Sobolev method, the first part of the problem is solved, i.e., an explicit expression of the square of the norm of the error functional of the optimal interpolation formulas in the Hilbert space W2(2,0) is found.

Keywords

• optimal interpolation formulas
• the error functional
• the extremal function
• hilbert space
• оптимальные интерполяционные формулы
• функционал погрешности
• экстремальная функция
• гильбертово пространство