An algorithm and stability theory for downdating the ULV decomposition (Q1913582)

Special factorizations of \(A\in\mathbb{R}^{m \times n}\) \((m\geq n)\) of the form \(A=U {C\brack 0} V^T\) are considered, where \(U \in\mathbb{R}^{m \times m}\), \(V \in\mathbb{R}^{n \times n}\) are orthogonal, \(C \in R^{n\times n}\) is a lower triangular matrix. They serve as a means to separate the subspace associated with ``large'' and ``small'' singular values of \(A\). In some statistical problems it is desirable to delete a row from \(A\) and its factorized form (this is downdating). A special algorithm is suggested to preserve (in a sense) the structure in \(C\). A stability analysis is given with respect to round-off errors.