Lagrange Interpolation and Quadrature Formula in Rational Systems
نویسندگان
چکیده
منابع مشابه
On quadrature convergence of extended Lagrange interpolation
Quadrature convergence of the extended Lagrange interpolant L2n+1f for any continuous function f is studied, where the interpolation nodes are the n zeros τi of an orthogonal polynomial of degree n and the n+ 1 zeros τ̂j of the corresponding “induced” orthogonal polynomial of degree n + 1. It is found that, unlike convergence in the mean, quadrature convergence does hold for all four Chebyshev w...
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where > 0. Once the theory had been developed in its entirety, it became clear that one could simultaneously treat not only weights like those above, but also not necessarily even weights on a general real interval. See [3], [12], [16] for various perspectives on this type of potential theory and its applications. One important application is to Lagrange interpolation. Mean convergence of Lagra...
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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: Journal of Approximation Theory
سال: 1998
ISSN: 0021-9045
DOI: 10.1006/jath.1997.3214