The Lagrange representation of the interpolating polynomial can be rewritten in two more computationally attractive forms: a modified Lagrange form and a barycentric form. We give an error analysis of the evaluation of the interpolating polynomial using these two forms. The modified Lagrange formula is shown to be backward stable. The barycentric formula has a less favourable error analysis, bu...

We continue the investigation initiated by Mastroianni and Szabados on question whether Jackson’s order of approximation can be attained by Lagrange interpolation for a wide class of functions. Improving a recent result of Mastroianni and Szabados, we show that for a subclass of C functions the local order of approximation given by Lagrange interpolation can be much better (of at least O()) tha...

In this paper, Lagrange interpolation in Chebyshev-Gauss-Lobatto nodes is used to develop a procedure for finding discrete and continuous approximate solutions of a singular boundary value problem. At first, a continuous time optimization problem related to the original singular boundary value problem is proposed. Then, using the Chebyshev- Gauss-Lobatto nodes, we convert the continuous time op...

In this paper a parallel algorithm for Lagrange interpolation is applied on a n-pancake graph. The npancake graph is a Cayley graph with N=n! vertices and with attractive properties regarding degree, diameter, symmetry, embeddings and self similarity. Using these properties the algorithm carries the calculation in O(N) steps of communication and arithmetic operations instead of O(N) steps for a...

In 1918 Bernstein [2] published a result concerning the divergence of Lagrange interpolation based on equidistant nodes. This result, which now has a prominent place in the study of the appoximation of functions by interpolation polynomials, may be described as follows. Throughout this paper let / (* ) = |x| (—1 < x < 1) and Xk,n = 1 + 2(fcl ) / ( n l ) (Jfe = 1,2,... ,n; n = 1 ,2 ,3 , . . . ) ...