The biglm package for R currently uses incremental QR decomposition, which fits linear models to big data in linear time and bounded memory, but doesn’t parallelize.

It turns out that parallel computation is easy (and has been studied by Dongarra and the LAPACK folks). If you have two data chunks reduced to \(R_1\) and \(Q_1^TY_1\), and \(R_2\) and \(Q_2^TY_2\), just treat each \(R\) as an \(X\) and each \(Q^TY\) as a \(Y\) to merge the QR decompositions.

So, if you have a file system that can feed \(M\) separate QR decomposition processes, you can do the QR decomposition in \(M\) parallel processes and then \(\log M\) sets of parallel merges.

Coming to the biglm package Real Soon Now.