I have a nxn covariance matrix (so, real, symmetric, dense, nxn... I mean positive semi-definite). 'n' may be very very very big! I'd like to solve partial (3 largest) eigenvalue (+eigenvectors) problem for this matrix. Could somebody tell me what the fastest algorithm to do it?Is it power iteration method (because it have O(n^2) complexity)?P.S. I'd like to make GPGPU implementation using OpenCL. 
Algorithm for Eigenvalue Problem of a Real Symmetric nxn Matrix
linear algebra;eigensystem;gpu;eigenvalues