Asymptotic Properties of Collocation Matrix Norms 1: Global Polynomial Approximation
K. Wright · IMA Journal of Numerical Analysis · 1984
This paper shows that a matrix related to the n-point collocation solution of mth order ordinary differential equations using global polynomials has maximum norm which tends, as n → to the maximum norm of an operator related to the differential equation if the collocation points are chosen as the zeros of certain orthogonal polynomials. The results justify a simple a posteriori estimate for the error in the mth derivative of the corresponding solution. This result is a consequence of a stronger result that the norm of the difference between the matrix mentioned above and another matrix associated with the differential equation tends to zero as n →.