Izvestiya of Saratov University.
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


Everywhere divergence of Lagrange processes on the unit circle

We study the convergence of Lagrange interpolation processes in the closed unit disk. Choosing a matrix with a certain distribution of interpolation nodes allowed to construct the set, completely covering the unit circle, and the function for which the process diverges everywhere on this set.

Method of Hermite Interpolation by Polynomials of the Third Degree on a Triangle Using Mixed Derivatives

There is a sine of the minimum angle of the triangle in the denominator of estimation of inaccuracy of interpolation for derivative of function in building of triangular finite elements. The way of method of Hermite interpolation by polynomials of the third degree on a triangle suggested by N.V. Baidakova is free of minimum angle condition for approximation of any derivatives. There is two-dimenetional cubic element in finite element method equal to element of N.V. Baidakova in this paper.

Interpolation by the Simplest Fractions

The interpolation by means of real simplest fractions is considered. There are offered a different ways of intepolating simpest fractions construction with distinct real nodes. Necessary and sufficient conditions of existence and uniqueness of interpolating simplest fractions are received. Interpolation of constants is in detail investigated; in this case the estimation of an error of interpolation on Chebyshev‘s system of nodes is received.

Some Properties of 0/1-Simplices

Let n ∈ N, and let Q n = [0,1] n . For a nondegenerate simplex S ⊂ R n , by σS we mean the homothetic copy of S with center of homothety in the center of gravity of S and ratio of homothety σ. Put ξ(S) = min{σ > 1 : Q n ⊂ σS}, ξ n = min{ξ(S) : S ⊂ Q n }.