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%Mart{\'\i}nez
%Jos\'e-Javier","jjavier.martinez@uah.es","
\section{Polynomial regression in the Bernstein basis} By {\sl Ana Marco, Jos\'e-Javier Mart{\'\i}nez}.  

\medskip  \noindent The problem of polynomial regression in which the usual monomial basis is replaced by the Bernstein basis is considered. The coefficient matrix $A$ of the overdetermined system to be solved in the least-squares sense is then a rectangular Bernstein-Vandermonde matrix. In order to use the method based on the QR decomposition which was developed in the celebrated paper [1], the first stage will consist of computing the bidiagonal decomposition of the coefficient matrix $A$ by means of an extension to the rectangular case of the algorithm presented in [3]. Starting from that bidiagonal decomposition, an algorithm for obtaining the QR decomposition of $A$ due to Koev [2] is then applied. Finally, a triangular system is solved by using the bidiagonal decomposition of the $R$-factor of $A$. Some numerical experiments showing the behaviour of our approach are included.  \bigskip [1] G. Golub: Numerical methods for solving linear least squares problems. Numerische Mathematik 7, 206-216 (1965). \medskip [2] P. Koev: Accurate computations with totally nonnegative matrices. SIAM J. Matrix Anal. Appl. 29(3), 731-751 (2007). \medskip [3] A. Marco, J.-J. Mart{\'\i}nez: A fast and accurate algorithm for solving Bernstein-Vandermonde linear systems. Linear Algebra Appl. 422, 616-628 (2007)
%Least squares;  Bernstein basis; Bidiagonal decomposition","65F05","65F20","","05:19:13","Fri Mar 14 2008","212.128.76.118"
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