Out-of-Core Singular Value Decomposition

Traditional Singular Value Decomposition usually applies an \in-core" computation, that is, all the matrix components must be loaded into memory before the computation can start, unless some distributed schemes are involved where communication among several machines may be necessary. While matrix size can easily exceed the memory capacity and becomes nearly comparable to the disk space, the naive approach of using automatic virtual memory support from the underlying operating system may be infeasible. We address this issue by implementing a system which is capable of doing Out-of-Core Singular Value Decomposition and performing simple Fold-In updates of rows and columns. Using modern PCs equipped with as few as 64 MB memory capacity, our out-of-core algorithm can be applied to a matrix as big as 5 million rows by 5 million columns. A simple metric for deciding the lost of accuracy caused by the Fold-In update process is also proposed and veriied. This metric serves as a hint for tolerating continuous updates or suggesting users the necessity of a SVD re-computation. Due to various applications of SVD, we have further provided a general purposed interface to facilitate its use for other packages.