Nous utilisons les interpolations de Kergin et d'Hakopian pour construire des bases du dual de l'espace des polynômes harmoniques à deux variables.
We use Kergin and Hakopian interpolants to give some bases for the dual space of bivariate harmonic polynomials.
Accepté le :
Publié le :
Phung Van Manh 1
@article{CRMATH_2017__355_1_28_0, author = {Phung Van Manh}, title = {On polynomial interpolation of bivariate harmonic polynomials}, journal = {Comptes Rendus. Math\'ematique}, pages = {28--33}, publisher = {Elsevier}, volume = {355}, number = {1}, year = {2017}, doi = {10.1016/j.crma.2016.11.008}, language = {en}, }
Phung Van Manh. On polynomial interpolation of bivariate harmonic polynomials. Comptes Rendus. Mathématique, Volume 355 (2017) no. 1, pp. 28-33. doi : 10.1016/j.crma.2016.11.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.11.008/
[1] Spline Functions and Multivariate Interpolations, Springer-Verlag, 1993
[2] Kergin interpolant at the roots of unity approximate functions, J. Anal. Math., Volume 72 (1997), pp. 203-221
[3] The polynomial projectors that preserve homogeneous differential relations: a new characterization of Kergin interpolation, East J. Approx., Volume 10 (2004), pp. 441-454
[4] Interpolation of harmonic functions bases on Radon projections, Numer. Math., Volume 127 (2014), pp. 423-445
[5] New results on regularity and errors of harmonic interpolation using Radon projections, J. Comput. Appl. Math., Volume 29 (2016), pp. 73-81
[6] Interpolation in minimum seminorm and multivariate B-spline, J. Approx. Theory, Volume 37 (1983), pp. 212-223
[7] Multivariate divided differences and multivariate interpolation of Lagrange and Hermite type, J. Approx. Theory, Volume 34 (1982), pp. 286-305
[8] A constructive approach to Kergin interpolation in : multivariate B-spline and Lagrange interpolation, Rocky Mt. J. Math., Volume 10 (1980), pp. 485-497
[9] On the convergence of Kergin and Hakopian interpolants at Leja sequences for the disk, Acta Math. Hung., Volume 136 (2012), pp. 165-188
Cité par Sources :
Commentaires - Politique