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

Gemignani, Luca (1996) Fast QR Factorization of Vandermonde-like matrices involving orthogonal polynomials. Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

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} \bigskip