Stable Algorithms for Downdating Two-sided Orthogonal Decompositions

Download or read book Stable Algorithms for Downdating Two-sided Orthogonal Decompositions written by Jesse Louis Barlow and published by . This book was released on 1993 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "A common alternative to performing the singular value decomposition is to factor a matrix A into A=U(C/O)V[superscript T] where U and V are orthogonal matrices and C is triangular matrix which indicates a separation between two subspaces by the size of its columns. These subspaces are denoted by V=(V1, V2) where the columns of C are partitioned conformally into C=(C1, C2) with [formula]. Here [epsilon] is some tolerance. If the matrix A results from statistical observations, it is often desired to remove old observations, thus deleting a row from C. In matrix terms, this is called a downdate. It is desired to preserve the structure of C to the extent possible. Downdating algorithms are proposed for the cases where C is either upper or lower triangular that preserve the above block structure in the downdated matrix C. Strong stability results are proven for these algorithms based upon a perturbation theory for updating and downdating such decomposition from earlier work."