  A generalization of the Vandermonde matrices which arise when the power basis
is replaced by the Said-Ball basis is considered. When the nodes are inside the
interval (0,1), then those matrices are strictly totally positive. An algorithm
for computing the bidiagonal decomposition of those Said-Ball-Vandermonde
matrices is presented, which allows to use known algorithms for totally
positive matrices represented by their bidiagonal decomposition. The algorithm
is shown to be fast and to guarantee high relative accuracy. Some numerical
experiments which illustrate the good behaviour of the algorithm are included.
