如何快速准确地得到特征值和特征向量?

I need to compute the eigenvalues and eigenvectors of a big matrix (about 1000*1000 or even more). Matlab works very fast but it does not guaranty accuracy. I need this to be pretty accurate (about 1e-06 error is ok) and within a reasonable time (an hour or two is ok).I need to compute the eigenvalues and eigenvect