Parallel Dixon matrices by bracket (Q1397302)

The determinant of a Dixon matrix constructed for three bi-degree polynomials in two variables is an important computational tool in computer aided geometric design [cf. \textit{E.-W. Chionh}, Comput. Aided Geom. Des. 14, 561-570 (1997; Zbl 0896.65018)]. The entries of the Dixon matrix can be computed in parallel using an entry formula or by diagonal marching introduced by \textit{E. W. Chionh, M. Zhang} and \textit{R. N. Goldman} [J. Symb. Comput. 33, 13-29 (2002; Zbl 0996.65046)]. In this paper a new parallel method for constructing the Dixon matrix by bracket is presented and compared with the previously introduced methods. The author proves that the Dixon matrix has a total of \(m(m+1)^{2}(m+2)n(n+1)^{2}(n+2)/36\) brackets but only \(mn(m+1)(n+1)(mn+2m+2n+1)/6\) of them are distinct. The main corollary is that the new algorithm is the fastest but it requires the biggest number of processors.