strassen的矩阵乘法在哪里有用?

问题描述

Strassen的矩阵乘法算法仅比常规的O(N^3)算法有一点点改进.它具有较高的恒定因子，很难实施.鉴于这些缺点，strassens算法实际上有用吗，是否可以在任何库中实现矩阵乘法?而且，如何在库中实现矩阵乘法?

Strassen's algorithm for matrix multiplication just gives a marginal improvement over the conventional O(N^3) algorithm. It has higher constant factors and is much harder to implement. Given these shortcomings, is strassens algorithm actually useful and is it implemented in any library for matrix multiplication? Moreover, how is matrix multiplication implemented in libraries?

推荐答案

通常，由于以下原因，实际应用中不建议使用Strassen方法.

Generally Strassen’s Method is not preferred for practical applications for following reasons.

1. 斯特拉森方法中使用的常数很高，对于典型的应用，朴素方法效果更好.
2. 对于稀疏矩阵，有专门设计的更好方法为他们.
3. 递归子矩阵占用额外的空间.
4. 由于计算机运算的精度有限非整数值，更大的错误会在Strassen的算法中累积比天真的方法要好.

1. The constants used in Strassen’s method are high and for a typical application Naive method works better.
2. For Sparse matrices, there are better methods especially designedfor them.
3. The submatrices in recursion take extra space.
4. Because of the limited precision of computer arithmetic onnoninteger values, larger errors accumulate in Strassen’s algorithmthan in Naive Method.

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