Hermite pseudospectral approximations. An error estimate (Q1772296)

The objective of the paper is to estimate the norm of the error of the pseudospectral approximation in certain weighted Sobolev spaces [see \textit{D. Funaro} and \textit{O. Kavian}, Math. Comput. 57, 597--619 (1991; Zbl 0764.35007)]. The authors give here a bound for the error of the pseudospectral approximation which is sharper than the corresponding bound given in an earlier paper [cf. \textit{B.-Y. Guo} and \textit{C.-L. Xu}, Math. Model. Numer. Anal. 34, 859--872 (2000; Zbl 0966.65072)].