منابع مشابه
On Multivariate Lagrange Interpolation
Lagrange interpolation by polynomials in several variables is studied through a finite difference approach. We establish an interpolation formula analogous to that of Newton and a remainder formula, both of them in terms of finite differences. We prove that the finite difference admits an integral representation involving simplex spline functions. In particular, this provides a remainder formul...
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Barycentric interpolation is a variant of Lagrange polynomial interpolation that is fast and stable. It deserves to be known as the standard method of polynomial interpolation.
متن کاملOn Lagrange Interpolation with Equidistant Nodes
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 , . . . ) ...
متن کاملOn Boundedness of Lagrange Interpolation
We estimate the distribution function of a Lagrange interpolation polynomial and deduce mean boundedness in Lp; p < 1: 1 The Result There is a vast literature on mean convergence of Lagrange interpolation, see [4{ 8] for recent references. In this note, we use distribution functions to investigate mean convergence. We believe the simplicity of the approach merits attention. Recall that if g : R...
متن کاملConvergence of Extended Lagrange Interpolation
The authors give a procedure to construct extended interpolation formulae and prove some uniform convergence theorems.
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1994
ISSN: 0377-0427
DOI: 10.1016/0377-0427(94)90299-2