4.2 Strassen's algorithm for matrix multiplication: Strassen's algorithm 是关于两个 n×n 矩阵乘法的算法。该算法将矩阵乘法一般算法的 Θ(n3) 时间复杂度降低为 O(nlg7)。 首先我们来看矩阵乘法一般算法。定义两个 n×n 的矩阵 A=(aij) 和B=(bij) ,定义矩阵 C=A∗B。对于 1<=i<=n,1<=j<=...
squre_matrix_multiply(A,B)结果:[[8, 10], [21,24]] 通过分治思想求解: 分治思想: 将 N x N 划分为4 个 N/2 * N/2的子矩阵乘积之和.defsqure_matrix_multiply_recursive(A, B):try: n=len(A[0])exceptTypeError: n= 1#let c to be a new nxn matrixc = [[0forxinrange(n)]foryin...
https://www.youtube.com/watch?v=sB-Dh4DsOy0 学完Cannon算法之后给好友讲解的时候,说着我想做这样一个视频,然后!好友找到了这个我的视频想法的具体实现!知识 校园学习 转载 并行算法 Cannon算法 卡农算法 Cannon's algorithm 紧扣的dagger 发消息 云存储区up主、行为艺术家&精神病患者、已婚、外骨骼健身中、...
toeplitz-block matrixgramianWe design a new parallel algorithm for matrix multiplication by Gramian of Toeplitz-block matrix. This type of computation represents the computationally most intensive task in the iterativ e methods for the singular v alue decomposition of data matr...
如果感觉对算法细节仍然不够清晰的话,建议观看up主转载的视频(可看简介):Cannon's algorithm for matrix multiplication - YouTube转载,在给up主的好友讲解的时候,up主就想制作这样一个动画,没想到youtube上已经有人做了,用不同颜色清晰区别出P_ij节点之间所需的分块矩阵数据!
Steps of Strassen’s matrix multiplication: Divide the matrices A and B into smaller submatrices of the size n/2xn/2. Using the formula of scalar additions and subtractions compute smaller matrices of size n/2. Recursively compute the seven matrix products Pi=AiBi for i=1,2,…7. ...
J. Norstad, " MapReduce Algorithm for Matrix Multiplication," http://homepage. mac.com/j.norstad/matrix-multiply/index.html, 2009.J. Norstad. "A MapReduce Algorithm for Matrix Multiplication," 2010; http://homepage.mac.com/j.norstad/matrix-multiply/index.html....
Cannon's algorithm is a memory-efficient matrix multiplication technique for parallel computers with toroidal mesh interconnections. This algorithm assumes that input matrices are block distributed, but it is not clear how it can deal with block-cyclic distributed matrices. This paper generalizes Cannon...
answer, that the running time of the straightforward [inaudible] algorithm runs in cubic time relative to the matrix dimension n. To see this let's just recall what the definition of the matrix multiplication was. The definition tells us each entry zij of the output matrix z is defined as ...
For simplicity we fix k = F, for some arbitrary field F, so we will drop it from the notation and for the most part ignore it.Trivially, 2 ≤ω≤ 3. The upper bound follows from the grade school algorithm for matrix multiplication and the lower bound follows because the output is of...