The Implicitly Restarted Lanczos Bidiagonalization Algorithm (IRLBA) of Jim Baglama and Lothar Reichel is a state of the art method for computing a few singular vectors and corresponding singular values of huge matrices.
The IRLBA package is the R language implementation of the method. With it, you can compute partial SVDs and principal component analyses of very large scale data. The package works well with sparse matrices and with other matrix classes like those provided by the Bigmemory package.
In Video Vignette Link I have inserted below Bryan with a new microphone goes through an example using this package on the Netflix Prize data set (480K row by 18K columns). Competitions like the Netflix Prize and the Kaggle.com competitions have really brought powerful tools like SVD into greater use.
Video Vignette or IRLBA using the Netflix Prize data set.