Accuracy of singular vectors obtained by projection-based SVD methods
An alternative approach for the computation of an approximate SVD of a large-scale matrix is proposed in this paper. The numerical approach of an SVD of a large-scale matrix is based on its projection onto lower-dimensional trial subspaces from both sides and the computation of the SVD of the small projected matrix that is again projected back to the original space. Following this basic approach, a low-rank approximate SVD to the original matrix is obtained and by extracting subsets from the approximate SVD, the approximate left and right singular subspaces are determined. The authors propose the estimation of the quality of the extraction process of the subsets from the approximate SVD in terms of the accuracy of the approximate singular subspaces, measured by the angle between the exact and extracted subspaces in relation to the angle between the exact and trial subspaces. This estimation leads to the conclusion that the extracted approximate subspaces are optimal usually to within a modest constant.
scientific article; zbMATH DE number 6825307