We describe an algorithm for constructing a Lagrange interpolation pair based on C cubic splines defined on tetrahedral partitions. In particular, given a set of points V ∈ IR, we construct a set P containing V and a spline space S 3 (△) based on a tetrahedral partition △ whose set of vertices include V such that interpolation at the points of P is well-defined and unique. Earlier results are e...

In this paper,we deeply research Lagrange interpolation of n-variables and give an application of Cayley-Bacharach theorem for it. We pose the concept of sufficient intersection about s(1 ≤ s ≤ n) algebraic hypersurfaces in n-dimensional complex Euclidean space and discuss the Lagrange interpolation along the algebraic manifold of sufficient intersection. By means of some theorems ( such as Bez...

In this paper properties of cell matrices are studied. A determinant of such a matrix is given in a closed form. In the proof a general method for determining a determinant of a symbolic matrix with polynomial entries, based on multivariate polynomial Lagrange interpolation, is outlined. It is shown that a cell matrix of size n > 1 has exactly one positive eigenvalue. Using this result it is pr...

This paper gives an ecient numerical method for solving the nonlinear systemof Volterra-Fredholm integral equations. A Legendre-spectral method based onthe Legendre integration Gauss points and Lagrange interpolation is proposedto convert the nonlinear integral equations to a nonlinear system of equationswhere the solution leads to the values of unknown functions at collocationpoints.

The authors give a procedure to construct extended interpolation formulae and prove some uniform convergence theorems.

Bounds are proved for the Stieltjes polynomial En+1, and lower bounds are proved for the distances of consecutive zeros of the Stieltjes polynomials and the Legendre polynomials Pn. This sharpens a known interlacing result of Szegö. As a byproduct, bounds are obtained for the Geronimus polynomials Gn. Applying these results, convergence theorems are proved for the Lagrange interpolation process...

In the present paper, both the perfect convergence for the Lagrange interpolation of analytic functions on [ − 1, 1] and the perfect convergence for the trigono-metric interpolation of analytic functions on [ − p, p] with period 2p are discussed.