Two Algorithms for the The Efficient Computation of Truncated Pivoted QR Approximations to a Sparse Matrix

Abstract

In this note we propose two algorithms to compute truncated pivoted QR approximations to a sparse matrix. One is based on the Gram--Schmidt algorithm, and the other on Householder triangularization. Both algorithms leave the original matrix unchanged, and the only additional storage requirements are arrays to contain the factorization itself. Thus, the algorithms are particularly suited to determining low-rank approximations to a sparse matrix. (Also cross-referenced as UMIACS-TR-98-12)