Two Iterative Algorithms for Computing the Singular Value Decomposition from Input/Output Samples

Terence D. Sanger Jet Propulsion Laboratory MS 303-310 4800 Oak Grove Drive Pasadena, CA 91109 Abstract The Singular Value Decomposition (SVD) is an important tool for linear algebra and can be used to invert or approximate matrices. Although many authors use "SVD" synonymously with "Eigenvector Decomposition"or "Principal Components Transform", it is important to realize that these other methods apply only to symmetric matrices, while the SVD can be applied to arbitrary nonsquare matrices. This property is important for applications to signal transmission and control. I propose two new algorithms for iterative computation of the SVD given only sample inputs and outputs from a matrix. Although there currently exist many algorithms for Eigenvector Decomposition (Sanger1989, for example), these are the first true samplebased SVDalgorithms. 1 INTRODUCTION The Singular Value Decomposition (SVD) is a method for writing an arbitrary nons quare matrix as the product of two orthogonal matrices and a diagonal matrix.