How is the complexity of PCA O(min(p^3,n^3))?

Question

I\'ve been reading a paper on Sparse PCA, which is: http://stats.stanford.edu/~imj/WEBLIST/AsYetUnpub/sparse.pdf

And it states that, if you have n data poin

Answer 1

Covariance matrix computation is O(p²n); its eigen-value decomposition is O(p³). So, the complexity of PCA is O(p²n+p³).

O(min(p³,n³)) would imply that you could analyze a two-dimensional dataset of any size in fixed time, which is patently false.