Parallel Svd{updating Using Approximate Rotations

In this paper a parallel implementation of the SVD{updating algorithm using approximate rotations is presented. In its original form the SVD{updating algorithm had numerical problems if no reorthogonalization steps were applied. Representing the orthogonal matrix V (right singular vectors) using its parameterization in terms of the rotation angles of n(n?1)=2 plane rotations these reorthogonalization steps can be avoided during the SVD-updating algorithm 18]. This results in a SVD{updating algorithm where all computations (matrix vector multiplication, QRD{updating, Kogbetliantz's algorithm) are entirely based on the evaluation and application of orthogonal plane rotations. Therefore, in this form the SVD{updating algorithm is amenable to an implementation using CORDIC{based approximate rotations. Using CORDIC{based approximate rotations the n(n?1)=2 rotations representing V (as well as all other rotations) are only computed to a certain approximation accuracy (in the basis arctan 2 i). All necessary computations required during the SVD{updating algorithm (exclusively rotations) are executed with the same accuracy, i.e., only r w (w: wordlength) elementary orthonormal {rotations are used per plane rotation. Simulations show the eeciency of the implementation using CORDIC{based approximate rotations.