ACCURACY OF TSVD SOLUTIONS COMPUTED FROM RANK-REVEALING DECOMPOSITIONS

Rank-revealing decompositions are favorable alternatives to the singul ar value decomposition (SVD) because they are faster to compute and ea sier to update. Although they do not yield all the information that th e SVD does, they yield enough information to solve various problems be cause they provide accurate bases for the relevant subspaces. In this paper we consider rank-revealing decompositions in computing estimates of the truncated SVD (TSVD) solution to an overdetermined system of l inear equations Ax approximate to b, where A is numerically rank defic ient. We derive analytical bounds which show how the accuracy of the s olution is intimately connected to the quality of the subspaces.