Low-rank revealing \(UTV\) decompositions (Q1370338)

Much attention has been paid to the \(UTV\) decompositions of a high-rank matrix, however, only a little to the low-rank case. Low-rank matrices arise when a small number of parameters suffices to describe a system. The high-rank revealing algorithms are not suited for such problems, and hence there is a need for algorithms which handle the low-rank case. The authors focus on \(ULV\) algorithms. Two algorithms for computing rank-revealing \(UTV\) decompositions of a low-rank matrix are presented and analyzed. These algorithms are suited for updating. Comparisons with two singular value decomposition algorithms and numerical examples are presented.