"eig"和"eigs"有什么区别? [英] What is the difference between 'eig' and 'eigs'?

问题描述

我为此进行了很多搜索，但是找不到关于"eig"和"eigs"这两种方法有何不同的答案.从它们接收到的特征值和特征向量之间有什么区别?

I've searched a lot for this but I can't find any answer about how the two methods 'eig' and 'eigs' differ. What is the difference between the eigenvalues and eigenvectors received from them?

推荐答案

他们使用不同的算法，针对不同的问题和不同的目标量身定制.

They use different algorithms, tailored to different problems and different goals.

eig是一个很好的，快速的，通用的特征值/向量求解器.当您的矩阵具有适合内存的实际大小，并且需要所有特征值/向量时，则适合使用此方法.稀疏矩阵在eig中根本不起作用.

eig is a good, fast, general use eigenvalue/vector solver. It is appropriate for use when your matrix is of a realistic size that fits well in memory, and when you need all of the eigenvalues/vectors. Sparse matrices do not work at all in eig.

Eigs是一种求解器，它更适合于仅需要特征值/向量的有限子集的情况.在这里，矩阵通常以稀疏格式存储，因为作为一个完整的矩阵，它将占用过多的内存来存储.似乎eigs基于 ARPACK .

Eigs is a solver that is more appropriate for when you need only a limited subset of the eigenvalues/vectors. Here the matrix is often stored in sparse format, because as a full matrix, it would take up too much memory to store. It appears that eigs is based on ARPACK.

如果您确实要询问有关实际算法的细节，那么这个问题显然不适合本网站.坐下来拿着矩阵计算"的副本，或者更好的是，阅读文档中列出的eigs的一对参考.

If you truly are asking for specifics on the actual algorithms, this is a question that is clearly inappropriate for this site. Sit down with a copy of "Matrix Computations", or better yet, read the pair of references listed in the doc for eigs.

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