The irlba package for
R provides a state of the art fast partial singular value decomposition. It's
suitable for very large scale problems and supports sparse and dense matrices.
To give you an idea how fast it is, one can compute a five-dimensional
principal components analysis (PCA) on the Netflix data set
(480,189 user IDs and 17,770 movies) in a few minutes on a dual-core notebook
(using R's sparse Matrix package).