The.Algorithm.Design.Manual.Springer-Verlag.1998

Matrix Multiplication
Next: Determinants and Permanents Up: Numerical Problems Previous: Bandwidth Reduction
Matrix Multiplication
Input description: An matrix A and a matrix B.
Problem description: The matrix .
Discussion: Although matrix multiplication is an important problem in linear algebra, its main
significance for combinatorial algorithms is its equivalence to a variety of other problems, such as
transitive closure and reduction, solving linear systems, and matrix inversion. Thus a faster algorithm for
matrix multiplication implies faster algorithms for all of these problems. Matrix multiplication arises in
its own right in computing the results of such coordinate transformations as scaling, rotation, and
translation for robotics and computer graphics.
The straightforward algorithm to compute the product of matrix A and matrix B runs in O(x y
z) time and is tough to beat in practice:
for i=1 to x do
file:///E|/BOOK/BOOK3/NODE138.HTM (1 of 4) [19/1/2003 1:30:18]