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Many important problems in pure and applied mathematics and engineering can be reduced to linear algebra on dense structured matrices. The structure of these dense matrices is understood in the sense that their n2 entries can be "compressed" to a smaller n ...
This paper presents an asymptotically stable scheme for the spectral approximation of linear conservation laws defined on a triangle. Lagrange interpolation on a general two-dimensional nodal set is employed and, by imposing the boundary conditions weakly ...
An efficient recursive solution is presented for the one-sided unconstrained tangential interpolation problem. The method relies on the triangular factorization of a certain structured matrix that is implicitly defined by the interpolation data. The recurs ...
We present a general Fourier-based method that provides an accurate prediction of the approximation error as a function of the sampling step T. Our formalism applies to an extended class of convolution-based signal approximation techniques, which includes ...
The electrostatic interpretation of the Jacobi-Gauss quadrature points is exploited to obtain interpolation points suitable for approximation of smooth functions defined on a simplex. Moreover, several new estimates, based on extensive numerical studies, f ...
Society for Industrial and Applied Mathematics1998
In this paper we apply the ideas of algebraic topology to the analysis of the finite volume and finite element methods, illuminating the similarity between the discretization strategies adopted by the two methods, in the light of a geometric interpretation ...
Based on the theory of approximation, this paper presents a unified analysis of interpolation and resampling techniques. An important issue is the choice of adequate basis functions. We show that, contrary to the common belief, those that perform best are ...
We propose a new method for the intermodal registration of images using a criterion known as mutual information. Our main contribution is an optimizer that we specifically designed for this criterion. We show that this new optimizer is well adapted to a mu ...
We extend the classical interpolation method to generalized interpolation. This extension is done by replacing the interpolating function by a non-interpolating function that is applied to prefiltered data, in order to preserve the interpolation condition. ...
The most essential ingredient of interpolation is its basis function. We have shown in previous papers that this basis need not be necessarily interpolating to achieve good results. On the contrary, several recent studies have confirmed that non-interpolat ...
