In this note we prove mean convergence of Lagrange interpolation at the zeros para-orthogonal polynomials for measures on unit circle which do not belong to Szegő’s class. When measure is in class, proved functions disk algebra.

In the present paper we will introduce a new approach to multivariate interpolation by employing polyharmonic functions as interpolants, i.e. by solutions of higher order elliptic equations. We assume that the data arise from C∞ or analytic functions in the ball BR. We prove two main results on the interpolation of C∞ or analytic functions f in the ball BR by polyharmonic functions h of a given...

Sparse-grid interpolation provides good approximations to smooth functions in high dimensions based on relatively few function evaluations, but in standard form is expressed in Lagrange polynomials and requires function values at all points of a sparse grid. Here we give a block-diagonal factorization of the matrix for changing basis from a Lagrange polynomial formulation of a sparse-grid inter...

In a multi-secret sharing scheme, several secret values are distributed among a set of n participants.In 2000 Chien et al.'s proposed a (t; n) multi-secret sharing scheme. Many storages and publicvalues required in Chien's scheme. Motivated by these concerns, some new (t; n) multi-secret sharingschemes are proposed in this paper based on the Lagrange interpolation formula for polynomials andcip...

Let X be a triangular array of interpolation points in a compact subset of [0; 2 ]. We obtain a necessary and su¢ cient condition for the existence of p > 0 such that the associated trigonometric polynomials are convergent in Lp. We also examine Lagrange interpolation on the unit circle. The results are analogues of our earlier ones for Lagrange interpolation on a real interval. 1. The Result I...