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  2. Strassen algorithm - Wikipedia

    en.wikipedia.org/wiki/Strassen_algorithm

    Strassen algorithm. 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.

  3. Computational complexity of matrix multiplication - Wikipedia

    en.wikipedia.org/wiki/Computational_complexity...

    C [i][j] = C [i][j] + A [i][k]* B [k][j] output C (as A*B) This algorithm requires, in the worst case, ⁠ ⁠ multiplications of scalars and ⁠ ⁠ additions for computing the product of two square n×n matrices. Its computational complexity is therefore ⁠ ⁠, in a model of computation where field operations (addition and multiplication ...

  4. Matrix multiplication algorithm - Wikipedia

    en.wikipedia.org/wiki/Matrix_multiplication...

    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 ...

  5. Matrix multiplication - Wikipedia

    en.wikipedia.org/wiki/Matrix_multiplication

    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 resulting matrix, known as the matrix product, has the number of rows of the ...

  6. Matrix chain multiplication - Wikipedia

    en.wikipedia.org/wiki/Matrix_chain_multiplication

    Matrix chain multiplication (or the matrix chain ordering problem[1]) is an optimization problem concerning the most efficient way to multiply a given sequence of matrices. The problem is not actually to perform the multiplications, but merely to decide the sequence of the matrix multiplications involved. The problem may be solved using dynamic ...

  7. Cannon's algorithm - Wikipedia

    en.wikipedia.org/wiki/Cannon's_algorithm

    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 ...

  8. Matrix (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Matrix_(mathematics)

    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 ...

  9. CYK algorithm - Wikipedia

    en.wikipedia.org/wiki/CYK_algorithm

    In computer science, the Cocke–Younger–Kasami algorithm (alternatively called CYK, or CKY) is a parsing algorithm for context-free grammars published by Itiroo Sakai in 1961. [1][2] The algorithm is named after some of its rediscoverers: John Cocke, Daniel Younger, Tadao Kasami, and Jacob T. Schwartz.