# Fast QR Factorization of Vandermonde-like matrices involving orthogonal polynomials

Fast orthogonalization schemes for m\times n Vandermonde matrices
V=(z_i^j), introduced by Demeure, are extended to compute both a
$QR$ factorization and an inverse QR factorization of
Vandermonde-like
matrices P=(p_j(z_i)) where the polynomials
p_j(z) satisfy a three-term
recurrence relation. In this way we are able
to solve least squares (LS)
problems
of the form
\begin{eqnarray*}
{\rm minimize } \ ||{\bf b}-P{\bf x}||_2
\end{eqnarray*}
using only O(mn) arithmetical operations and O(m) storage.
\end{abstract}
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