Issue No.10 - October (1981 vol.30)
null Nai-Kuan Tsao , Department of Computer Science, Wayne State University
The error complexity analysis of three algorithms for matrix multiplication and matrix chain product has been given. It is shown that the usual inner product type algorithm is by far the best algorithm for simple matrix multiplication or matrix chain product in terms of minimal basic term growth and minimal error complexities, the latter being independent of the order of pairwise matrix multiplications. Winograd's algorithm is comparable to the usual one, although in matrix chain product the error and data complexities are very sensitive to the order of pairwise matrix multiplication. Strassen's algorithm is not very attractive numerically for having the largest upper bound for both the maximum error complexity and the number of basic terms generated.
Winograd's algorithm, Data complexity, error complexity, floating-point arithmetic, matrix chain product, matrix multiplication, Strassen's algorithm
null Nai-Kuan Tsao, "Error Complexity Analysis of Algorithms for Matrix Multiplication and Matrix Chain Product", IEEE Transactions on Computers, vol.30, no. 10, pp. 758-771, October 1981, doi:10.1109/TC.1981.1675694