Friday July 29/1:30

MS60/Grande Ballroom

Theory and Applications of Rank Revealing Two-Sided (or Complete) Orthogonal Decompositions

A two-sided (or complete) orthogonal decomposition of a matrix, namely, the URV or ULV decomposition, provides the same rank information and nearly the same subspace information as the singular value decomposition SVD. While the highly regarded SVD is useful in many applications, it is considered computationally demanding and difficult to update/downdate in others. The URV or ULV decomposition is a reliable substitute to the SVD in various applications. In some problems, such as subspace tracking, a row of information is added or deleted from the middle matrix R or L and the decomposition must be correspondingly updated or downdated. In other problems, the numerical rank of the matrix is much less than the dimensions of the matrix, and this influences the choice of the algorithm. Further, when the matrix is sparse, the URV factorization can be modified to preserve the sparsity of R. In this minisymposium, the speakers will address some of these issues. Organizers: Ricardo Fierro California State University, San Marcos, and G. W. Stewart University of Maryland, College Park