SINGULAR VALUE DECOMPOSITION USING A JACOBI ALGORITHM WITH AN UNBOUNDED ANGLE OF ROTATION (CYCLIC, SVD, REAL SYMMETRIC)

This dissertation presents an investigation of the convergence of the cyclic Jacobi algorithm for use in the computation of the Singular Value Decomposition (SVD) of an arbitrary m x n matrix. For reference, it can be shown that this problem is equivalent to that of finding the eigenvalues and eigenvectors of a real symmetric matrix. This dissertation is presented in terms of SVD instead of the more traditional eigen-solution of a real symmetric matrix. The reason for this is that in recent years SVD has become increasingly popular in many fields of the applied sciences. This presentation considers the convergence of cyclic Jacobi methods using an unbounded angle of rotation. It provides a partial proof for the general case, two proofs for an m x 3 matrix, an analysis of the internal character of the "threshold" cyclic Jacobi method and a general proof of convergence of the threshold method.