  The accurate solution of some of the main problems in numerical linear
algebra (linear system solving, eigenvalue computation, singular value
computation and the least squares problem) for a totally positive
Bernstein-Vandermonde matrix is considered. Bernstein-Vandermonde matrices are
a generalization of Vandermonde matrices arising when considering for the space
of the algebraic polynomials of degree less than or equal to $n$ the Bernstein
basis, a widely used basis in Computer Aided Geometric Design, instead of the
monomial basis.
  Our approach is based on the computation of the bidiagonal factorization of a
totally positive Bernstein-Vandermonde matrix (or its inverse) by means of
Neville elimination. The explicit expressions obtained for the determinants
involved in the process makes the algorithm both fast and accurate.
