Out-of-Core SVD and QR Decompositions.

out-of-core singular-value-decomposition algorithm. The algorithm is designed for tall narrow matrices that are too large to fit in main memory and are stored on disks. We have implemented the algorithm and combined it with a larger eigensolver code to obtain the electronic states of a semiconductor nanocrystal. The computationalchemistry application requires finding an orthonormal basis for a subspace spanned by a small set of real vectors. The input typically consists of several hundreds to several thousands vectors whose length is between 200, 000–2, 000, 000. The orthonormal basis vectors are then used to reduce the dimensionality of an operator: given a matrix U of orthonormal basis vectors (U ’s columns) and a matrix H represented as a matrix-vector-multiplication routine, we compute Ĥ = U HU . We report on performance-evaluation runs on random matrices whose size ranges from 8 to 32GB and matches the size of the computational-chemistry application. Since neither the input matrix A (consisting of the original set of column vectors) nor the basis U fit in memory, we must store them on disks. We therefore use the following out-of-core strategy: