Error Complexity Analysis of Algorithms for Matrix Multiplication and Matrix Chain Product
IEEE Transactions on Computers
Sequential optimization of matrix chain multiplication relative to different cost functions
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
A coarse-grained parallel algorithm for the matrix chain order problem
Proceedings of the 2012 Symposium on High Performance Computing
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It is pointed out that the number of scalar multiplications (additions) required to evaluate a matrix chain product depends on the sequence in which the associative law of matrix multiplication is applied. An algorithm is developed to find the optimum sequence that minimizes the number of scalar multiplications. A program is written for use on the CDC 6600 computer to implement this algorithm and also to carry out the chain product according to the optimum sequence. Several examples are included to illustrate the algorithm. The saving in computation and improvement in accuracy that can result from the use of this algorithm can be quite significant for chain products of large arrays and in iterative solutions of matrix equations involving chain products.