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Error Complexity Analysis of Algorithms for Matrix Multiplication and Matrix Chain Product
October 1981 (vol. 30 no. 10)
pp. 758-771
| ASCII Text | x | ||
| 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. | |||
| BibTex | x | ||
| @article{ 10.1109/TC.1981.1675694, author = {null Nai-Kuan Tsao}, title = {Error Complexity Analysis of Algorithms for Matrix Multiplication and Matrix Chain Product}, journal ={IEEE Transactions on Computers}, volume = {30}, number = {10}, issn = {0018-9340}, year = {1981}, pages = {758-771}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1981.1675694}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Computers TI - Error Complexity Analysis of Algorithms for Matrix Multiplication and Matrix Chain Product IS - 10 SN - 0018-9340 SP758 EP771 EPD - 758-771 A1 - null Nai-Kuan Tsao, PY - 1981 KW - Winograd's algorithm KW - Data complexity KW - error complexity KW - floating-point arithmetic KW - matrix chain product KW - matrix multiplication KW - Strassen's algorithm VL - 30 JA - IEEE Transactions on Computers ER - | |||
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.
Index Terms:
Winograd's algorithm, Data complexity, error complexity, floating-point arithmetic, matrix chain product, matrix multiplication, Strassen's algorithm
Citation:
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, Oct. 1981, doi:10.1109/TC.1981.1675694
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