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Error Complexity Analysis of Algorithms for Matrix Multiplication and Matrix Chain Product
October 1981 (vol. 30 no. 10)
pp. 758771
ASCII Text  x  
null NaiKuan Tsao, "Error Complexity Analysis of Algorithms for Matrix Multiplication and Matrix Chain Product," IEEE Transactions on Computers, vol. 30, no. 10, pp. 758771, October, 1981.  
BibTex  x  
@article{ 10.1109/TC.1981.1675694, author = {null NaiKuan Tsao}, title = {Error Complexity Analysis of Algorithms for Matrix Multiplication and Matrix Chain Product}, journal ={IEEE Transactions on Computers}, volume = {30}, number = {10}, issn = {00189340}, year = {1981}, pages = {758771}, 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  00189340 SP758 EP771 EPD  758771 A1  null NaiKuan Tsao, PY  1981 KW  Winograd's algorithm KW  Data complexity KW  error complexity KW  floatingpoint 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, floatingpoint arithmetic, matrix chain product, matrix multiplication, Strassen's algorithm
Citation:
null NaiKuan Tsao, "Error Complexity Analysis of Algorithms for Matrix Multiplication and Matrix Chain Product," IEEE Transactions on Computers, vol. 30, no. 10, pp. 758771, Oct. 1981, doi:10.1109/TC.1981.1675694
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