@MISC{Hut_computationof, author = {T. C. Hut and M. T. Shing}, title = {COMPUTATION OF MATRIX CHAIN PRODUCTS. PART II*}, year = {} }

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Abstract

Abstract. This paper considers the computation of matrix chain products of the form M1 M2 " Mn-1. If the matrices are of different dimensions, the order in which the matrices are computed affects the number of operations. An optimum order is an order which minimizes the total number of operations. Some theorems about an optimum order of computing the matrices have been presented in Part [SIAM J. Comput., 11 (1982), pp. 362-373]. Based on those theorems, an O(n log n) algorithm for finding the optimum order is presented here. 1. Introduction. In Part I of this paper [6], we have transformed the matrix chain product problem into the optimum partitioning problem and have stated several theorems about the optimum partitions of an n-sided convex polygon. Some theorems in Part I can be strengthened and are stated here (the detailed proofs are in [7]). THEOREM 1. For every choice of V1, VE, (as prescribed in Part I), if the weights