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Iterative algorithm. 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: Input: matrices A ...
In linear algebra, the Strassen algorithm, named after Volker Strassen, is an algorithm for matrix multiplication. It is faster than the standard matrix multiplication algorithm for large matrices, with a better asymptotic complexity, although the naive algorithm is often better for smaller matrices.
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 ...
The result matrix has the number of rows of the first and the number of columns of the second matrix. 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 matrix–vector multiplication can be done in () arithmetical operations where is the average number of nonzero elements in a row. The total complexity is thus O ( d m n ) {\displaystyle O(dmn)} , or O ( d n 2 ) {\displaystyle O(dn^{2})} if m = n {\displaystyle m=n} ; the Lanczos algorithm can be very fast for sparse matrices.
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 -dimensional Boolean vector. The hardness of OuMv is implied by the hardness of OMv.
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] While Cannon's algorithm works well in homogeneous 2D grids, extending it to heterogeneous 2D grids ...
Matrix (mathematics) An m × n matrix: the m rows are horizontal and the n columns are vertical. Each element of a matrix is often denoted by a variable with two subscripts. For example, a2,1 represents the element at the second row and first column of the matrix. In mathematics, a matrix (pl.: matrices) is a rectangular array or table of ...