Evaluating phylogenetic trees by matrix decomposition

In this paper we begin by examining two currently used methods which solve matrices of pairwise distances in terms of additive trees, one proposed by Fitch and Margoliash (1967) and the other proposed by Saitou and Nei (1987). Neither method is exhaustive in the sense that not all possible trees are tested to ensure that the best solution has been reached. We develop a method here which decomposes any unrooted binary tree with a specified topology by a pair of matrices. Also, this method can generate trees using matrices. Thus it can be efficiently implemented on computers. Once the best solution is found by standard matrix techniques, the matrices can be recomposed into tree form.