Abstract
In this paper we carry over the Björck-Pereyra algorithm for solving Vandermonde linear systems to what we suggest to call Szegö-Vandermonde systems V Φ( x), i.e., polynomial-Vandermonde systems where the corresponding polynomial system Φ is the Szegö polynomials. The properties of the corresponding unitary Hessenberg matrix allow us to derive a fast O( n 2) computational procedure. We present numerical experiments that indicate that for ill-conditioned matrices the new algorithm yields better forward accuracy than Gaussian elimination.
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