Jacobi and Laguerre quasi-orthogonal approximations and related interpolations

Abstract

In this paper, we investigate Jacobi quasi-orthogonal approximation and generalized Jacobi-Gauss-Lobatto interpolation. We also propose Laguerre quasi-orthogonal approximation and generalized Laguerre-Gauss-Radau interpolation. A series of sharp results on these approximations are established, which are applicable to spectral and pseudospectral methods for mixed nonhomogeneous boundary value problems of high order.