منابع مشابه
Barycentric Lagrange Interpolation
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 کاملThe numerical stability of barycentric Lagrange interpolation
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...
متن کاملBarycentric Lagrange Interpolation As discussed by Jean-Paul Berrut and Lloyd N. Trefethen (2004)
This text discusses barycentric Lagrange interpolation based on the SIAM REVIEW article of Jean-Paul Berrut and Lloyd N. Trefethen [1]. It also offers additional background information, as well as some MATLAB demonstrations. Interpolation Given a set Dn of n + 1 nodes x j with corresponding values f j where j = 0, . . . ,n, we aim to construct the polynomial that satisfies p(x j) = f j j = 0, ....
متن کاملStability of Barycentric Interpolation Formulas
The barycentric interpolation formula defines a stable algorithm for evaluation at points in [−1, 1] of polynomial interpolants through data on Chebyshev grids. Here it is shown that for evaluation at points in the complex plane outside [−1, 1], the algorithm becomes unstable and should be replaced by the alternative modified Lagrange or “first barycentric” formula dating to Jacobi in 1825. Thi...
متن کاملOn 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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ژورنال
عنوان ژورنال: SIAM Review
سال: 2004
ISSN: 0036-1445,1095-7200
DOI: 10.1137/s0036144502417715