ABSTRACT
An important problem arising in a number of applications is to determine the rank of a matrix that has been contaminated with error and find an approximation to its null space. Traditionally the singular value decomposition or the pivoted QR decomposition has been used to solve this problem. However, both decompositions resist updating and parallelization. To circumvent these drawbacks, a new class of decompositions has been proposed. They factor the matrix in question into the product of an orthogonal matrix, a triangular matrix, and another orthogonal matrix. These UTV decompositions can be efficiently updated, both sequentially and in parallel. This paper is an informal introduction to UTV decompositions.
