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...
Figure 1 Matrix Multiplication 假如在矩阵 A 和矩阵 B 中, m=p=n=N ,那么完成 C=AB 需要多少次乘法呢? 对于每一个行向量 r ,总共有 N 行; 对于每一个列向量 c ,总共有 N 列; 计算它们的内积,总共有 N 次乘法计算。 综合可以看出,矩阵乘法的算法复杂度是:Θ(N3)。 二、Strassen算法 那么有没有...
From the above we see that simple matrix multiplication takes eight recursion calls. T(n)=O(n^3) Thus, this method is faster than the ordinary one. It takes only seven recursive calls, multiplication of n/2xn/2 matrices and O(n^2) scalar additions and subtractions, giving the below re...
Strassen's methodWe present a parallel method for matrix multiplication on distributed-memory MIMD architectures based on Strassen's method. Our timing tests, performed on a 56-node Intel Paragon, demonstrate the realization of the potential of the Strassen's method with a complexity of 4.7 M...
一共有8个(n/2)(n/2)的矩阵乘法和,4个(n/2)(n/2)的矩阵加法。再次使用以前的Master Method, T(n) = 8T(n/2) + T(n^2) 由此可见,算法的时间复杂度并没有下降,怎么办呢?? 下面就到了伟大的Strassen’s Idea了。谁也不知道他是怎么想出来这个算法的,但是呢,一个指导思想是,要想降低算法的时...
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 the sum from k=1 to n of. Xik times YKJ. That is the [inaudible] product of the [inaudible] row of the X matric and ...
3) matrix multiplication of strassen Strassen矩阵乘法 1. In this paper,we present an improved digital image watermarking method of singular value based on matrix multiplication of strassen and comparability measurement between original image and watermarking image;the new method is compared to the ...
We present a new method for accelerating matrix multiplication asymptotically. This work builds on recent ideas of Volker Strassen, by using a basic trilin... D Coppersmith,S Winograd - DBLP 被引量: 4428发表: 1987年 Matrix multiplication via arithmetic progressions A matrix multiplication algorithm...
C#,数值计算,矩阵相乘的斯特拉森(Strassen’s Matrix Multiplication)分治算法与源代码 矩阵乘法是机器学习中最基本的运算之一,对其进行优化是多种优化的关键。通常,将两个大小为N X N的矩阵相乘需要N^3次运算。从那以后,我们在更好、更聪明的矩阵乘法算法方面取得了长足的进步。沃尔克·斯特拉森于1969年首次发表了他...
在段然、周任飞和 Hongxun Wu 的第一篇论文《Faster Matrix Multiplication via Asymmetric Hashing》中,他们表明,施特拉森算法的进程可以大大加快。这一切要得益于他们称之为「隐藏损失」(hidden loss)的概念。周任飞表示,该概念深深地隐藏在以前的分析中,是无意中消除了太多块的结果。