算法导论 笔记2 4.2-矩阵乘法Strassen算法

4.2.1 使用Strassen计算

[1 3][6 8]
[7 5][4 2]

先手工算一下答案记下来

[18 14]
[62 66]

完全参考书的步骤来做一下这个题目

1. 分解矩阵 略

2. 创建并计算10个矩阵

      S1 = B12 - B22 = [6]
      S2 = A11 + A12 = [4]
      S3 = A21 + A22 = [12]
      S4 = B21 - B11 = [-2]
      S5 = A11 + A22 = [6]
      S6 = B11 + B22 = [8]
      S7 = A12 - A22 = [-2]
      S8 = B21 + B22 = [6]
      S9 = A11 - A21 = [-6]
      S10 = B11 + B12 = [14]
   

3. 计算7次矩阵乘法

    P1 = A11 * S1 = [6]
    P2 = S2 * B22 = [8]
    P3 = S3 * B11 = [72]
    P4 = A22 * S4 = [-10]
    P5 = S5 * S6 = [48]
    P6 = S7 * S8 = [-12]
    P7 = S9 * S10 = [-84]
   

4. 计算 C11 C12 C21 C22

    C11 = P5 + P4 - P2 + P6 = [18]
    C12 = P1 + P2 = [14]
    C21 = P3 + P4 = [62]
    C22 = P5 + P1 - P3 - P7 = [66]
   

没有纸笔, 靠我的脑子想不出来, 我先跳到第五章吧.