%0 Journal Article %1 berrut97:JCAM-78-355 %A Berrut, J. P. %A Mittelmann, H. %D 1997 %J Journal of Computational and Applied Mathematics %K usyd 65d04-interpolation 65d05-computational-geometric-interpolation 41a05-interpolation 41a20-approximation-by-rational-functions %N 2 %P 355--370 %R 10.1016/S0377-0427(96)00163-X %T Matrices for the Direct Determination of the Barycentric Weights of Rational Interpolation %U http://dx.doi.org/10.1016/S0377-0427(96)00163-X %V 78 %X Let x0,…,xN be N + 1 interpolation points (nodes) and 0,…,N be N + 1 interpolation data. Then every rational function r with numerator and denominator degress ⩽N interpolating these values can be written in its barycentric form completely determined by a vector u of N + 1 barycentric weights uk. Finding u is therefore an alternative to the determination of the coefficients in the canonical form of r; it is advantageous inasmuch as u contains information about unattainable points and poles. In classical rational interpolation the numerator and the denominator of r are made unique (up to a constant factor) by restricting their respective degrees. We determine here the corresponding vectors u by applying a stabilized elimination algorithm to a matrix whose kernel is the space spanned by the . The method is of complexity O(n3) in terms of the denominator degree n; it seems on the other hand to be among the most stable ones.

@article{berrut97:JCAM-78-355, abstract = {{Let x0,…,xN be N + 1 interpolation points (nodes) and 0,…,N be N + 1 interpolation data. Then every rational function r with numerator and denominator degress ⩽N interpolating these values can be written in its barycentric form completely determined by a vector u of N + 1 barycentric weights uk. Finding u is therefore an alternative to the determination of the coefficients in the canonical form of r; it is advantageous inasmuch as u contains information about unattainable points and poles. In classical rational interpolation the numerator and the denominator of r are made unique (up to a constant factor) by restricting their respective degrees. We determine here the corresponding vectors u by applying a stabilized elimination algorithm to a matrix whose kernel is the space spanned by the . The method is of complexity O(n3) in terms of the denominator degree n; it seems on the other hand to be among the most stable ones.}}, added-at = {2017-06-29T07:13:07.000+0200}, author = {Berrut, J. P. and Mittelmann, H.}, biburl = {https://www.bibsonomy.org/bibtex/2301a917e941ee05fa55755d1e1e097dd/gdmcbain}, citeulike-article-id = {2440932}, citeulike-attachment-1 = {berrut_97_matrices_1016726.pdf; /pdf/user/gdmcbain/article/2440932/1016726/berrut_97_matrices_1016726.pdf; 597a99f1303888d01d4ec9f9f3d9a13568fe7260}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/S0377-0427(96)00163-X}, doi = {10.1016/S0377-0427(96)00163-X}, file = {berrut_97_matrices_1016726.pdf}, interhash = {b3626ebc6dc8e1b82a5385eb28e298c8}, intrahash = {301a917e941ee05fa55755d1e1e097dd}, journal = {Journal of Computational and Applied Mathematics}, keywords = {usyd 65d04-interpolation 65d05-computational-geometric-interpolation 41a05-interpolation 41a20-approximation-by-rational-functions}, number = 2, pages = {355--370}, posted-at = {2008-02-28 10:09:52}, priority = {2}, timestamp = {2021-07-13T05:47:14.000+0200}, title = {{Matrices for the Direct Determination of the Barycentric Weights of Rational Interpolation}}, url = {http://dx.doi.org/10.1016/S0377-0427(96)00163-X}, volume = 78, year = 1997 }