Interpolation approximations based on Gauss–Lobatto–Legendre–Birkhoff quadrature
نویسندگان
چکیده
منابع مشابه
Interpolation approximations based on Gauss-Lobatto-Legendre-Birkhoff quadrature
We derive in this paper the asymptotic estimates of the nodes and weights of the Gauss-Lobatto-Legendre-Birkhoff (GLLB) quadrature formula, and obtain optimal error estimates for the associated GLLB interpolation in Jacobi weighted Sobolev spaces. We also present a useroriented implementation of the pseudospectral methods based on the GLLB quadrature nodes for Neumann problems. This approach al...
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Gaussian convolutions are perhaps the most often used image operators in low-level computer vision tasks. Surprisingly though, there are precious few articles that describe efficient and accurate implementations of these operators. In this paper we describe numerical approximations of Gaussian convolutions based on interpolation. We start with the continuous convolution integral and use an inte...
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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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Abstract. It is well-known that the trapezoidal rule, while being only second-order accurate in general, improves to spectral accuracy if applied to the integration of a smooth periodic function over an entire period on a uniform grid. More precisely, for the function that has a square integrable derivative of order r the convergence rate is o ( N−(r−1/2) ) , where N is a number of grid nodes. ...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2009
ISSN: 0021-9045
DOI: 10.1016/j.jat.2008.08.016