Bounds for the Structured Backward Errors of Vandermonde Systems
Jiguang Sun · SIAM Journal on Matrix Analysis and Applications · 1998
Consider the primal Vandermonde system V(a)x=b and the dual Vandermonde system V(a) T x=b, whereV(a) is the Vandermonde matrix defined in terms of the vector a =(\alpha_1, \ldots, \alpha_n)^T$ with distinct scalars $\alpha_1,\ldots, \alpha_n \in {\cal C}$. In view of the special structure of the matrix V(a), we define structured backward errors (SBEs) of the Vandermonde systems and describe a technique for obtaining upper and lower bounds for the SBEs. The results are illustrated by numerical examples.