Errors and Perturbations in Vandermonde Systems

The Bjorck-Pereyra algorithm for Vandermonde systems is known to produce extremely accurate results in some cases, even when the matrix is very ill-conditioned. Recently, Higham has produced an error analysis of the algorithm which identifies when this behaviour will take place. In this paper, we observe that this analysis also predicts the error behaviour very well in general, and illustrate this with a series of extensive numerical tests. Moreover, we relate the computational error to that caused by perturbations in the matrix elements, and show that they are not always commensurate. We also discuss the relationship between these error and perturbation estimates with the "effective well-condition" of Chan and Foulser.