Search results
Results from the WOW.Com Content Network
The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop:
Naïve matrix multiplication requires one multiplication for each "1" of the left column. Each of the other columns (M1-M7) represents a single one of the 7 multiplications in the Strassen algorithm. The sum of the columns M1-M7 gives the same result as the full matrix multiplication on the left.
In mathematics, specifically in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix.
The best known lower bound for matrix-multiplication complexity is Ω(n 2 log(n)), for bounded coefficient arithmetic circuits over the real or complex numbers, and is due to Ran Raz. [32] The exponent ω is defined to be a limit point, in that it is the infimum of the exponent over all matrix multiplication algorithms. It is known that this ...
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.
Due to the ubiquity of matrix multiplications in many scientific applications, including for the implementation of the rest of Level 3 BLAS, [21] and because faster algorithms exist beyond the obvious repetition of matrix-vector multiplication, gemm is a prime target of optimization for BLAS
The online vector-matrix-vector problem (OuMv) is a variant of OMv where the algorithm receives, at each round , two Boolean vectors and , and returns the product . This version has the benefit of returning a Boolean value at each round instead of a vector of an n {\displaystyle n} -dimensional Boolean vector.
In computer science, Cannon's algorithm is a distributed algorithm for matrix multiplication for two-dimensional meshes first described in 1969 by Lynn Elliot Cannon. [ 1 ] [ 2 ] It is especially suitable for computers laid out in an N × N mesh. [ 3 ]