  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 of A, the first stage consists of computing the bidiagonal
decomposition of the coefficient matrix A. Starting from that bidiagonal
decomposition, an algorithm for obtaining the QR decomposition of A is the
applied. Finally, a triangular system is solved by using the bidiagonal
decomposition of the R-factor of A. Some numerical experiments showing the
behavior of this approach are included.
