Parallel Dixon matrices by bracket

Abstract

It is known that the Dixon matrix can be constructed in parallel either by entry or by diagonal. This paper presents another parallel matrix construction, this time by bracket. The parallel by bracket algorithm is the fastest among the three, but not surprisingly it requires the highest number of processors. The method also shows analytically 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.