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Strass递归算法求矩阵乘法

2013-06-10 14:23:09| 分类： M&M | 标签： |举报 |字号大中小订阅

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采用递归方式实现，MATLAB函数如下：

function C=strass(A,B,n,n_min)
    if n<=n_min
              C=A*B;

       else
              m=n/2;
              u=1:m;
              v=m+1:n;
              P1=strass(A(u,u)+A(v,v),B(u,u)+B(v,v),m,n_min);
              P2=strass(A(v,u)+A(v,v),B(u,u),m,n_min);
              P3=strass(A(u,u),B(u,v)-B(v,v),m,n_min);
              P4=strass(A(v,v),B(v,u)-B(u,u),m,n_min);
              P5=strass(A(u,u)+A(u,v),B(v,v),m,n_min);
              P6=strass(A(v,u)-A(u,u),B(u,u)+B(u,v),m,n_min);
              P7=strass(A(u,v)-A(v,v),B(v,u)+B(v,v),m,n_min);
              C(u,u)=P1+P4+P7-P5;
              C(u,v)=P3+P5;
              C(v,u)=P2+P4;
              C(v,v)=P1+P3+P6-P2;
      end
end

理论上来讲，该算法比传统的算法效率会提高一些，相对于传统算法的O(n^3),该算法为O(n^2.807)，但是如果用程序实现，会比传统方法更耗时，因为大量采用递归会造成性能的显著下降。

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