In this project, new formulas for computing the bidiagonal decompositions of the Vandermonde, (q-,h-) Bernstein-Vandermonde, and other matrices, are presented. The new formulas allow for accurate computations to be made with the matrices, even when they are singular, which happens when two of their parameters are equal. They were obtained by factoring the diagonal matrices of the standard decompositions into many and grouping them with the lower bidiagonal matrices, cancelling the denominators which could possibly equal 0. Matlab programs were created as well, and they compute the decompositions at a quadratic computational cost.
Steven Ognyanov Spasov