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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:
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]
The following mathematical statements hold when A is a full rank square matrix: A^-1 *(A * x)==A^-1 * (b) (A^-1 * A)* x ==A^-1 * b (matrix-multiplication associativity) x = A^-1 * b. where == is the equivalence relational operator. The previous statements are also valid MATLAB expressions if the third one is executed before the others ...
In theoretical computer science, the computational complexity of matrix multiplication dictates how quickly the operation of matrix multiplication can be performed. Matrix multiplication algorithms are a central subroutine in theoretical and numerical algorithms for numerical linear algebra and optimization, so finding the fastest algorithm for matrix multiplication is of major practical ...
Freivalds' algorithm (named after Rūsiņš Mārtiņš Freivalds) is a probabilistic randomized algorithm used to verify matrix multiplication. Given three n × n matrices A {\displaystyle A} , B {\displaystyle B} , and C {\displaystyle C} , a general problem is to verify whether A × B = C {\displaystyle A\times B=C} .
The left column visualizes the calculations necessary to determine the result of a 2x2 matrix multiplication. 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 ...
Category: Matrix multiplication algorithms. ... Print/export Download as PDF; Printable version; In other projects
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 implementers.