C++ eigenvalue/vector decomposition, only need first n vectors fast

Question

I have a ~3000x3000 covariance-alike matrix on which I compute the eigenvalue-eigenvector decomposition (it\'s a OpenCV matrix, and I use cv::eigen() to get the job

Answer 1

In this article, Simon Funk shows a simple, effective way to estimate a singular value decomposition (SVD) of a very large matrix. In his case, the matrix is sparse, with dimensions: 17,000 x 500,000.

Now, looking here, describes how eigenvalue decomposition closely related to SVD. Thus, you might benefit from considering a modified version of Simon Funk's approach, especially if your matrix is sparse. Furthermore, your matrix is not only square but also symmetric (if that is what you mean by covariance-like), which likely leads to additional simplification.

... Just an idea :)