Sequential Optimization of Matrix Chain Multiplication Relative to Different Cost Functions

摘要

In this paper, we present a methodology to optimize matrix chain multiplication sequentially relative to different cost functions such as total number of scalar multiplications, communication overhead in a multiprocessor environment, etc. For n matrices our optimization procedure requires O(n~3) arithmetic operations per one cost function. This work is done in the framework of a dynamic programming extension that allows sequential optimization relative to different criteria.