On the efficient use of Givens rotations in SVD-based subspace tracking algorithms

In this paper, the issue of the efficient use of Givens rotations in SVD-based QR Jacobi-type subspace tracking algorithms is addressed. By relaxing the constraint of upper triangularity on the singular value matrix, we show how even fewer Givens rotations can achieve a better diagonalization and provide more accurate singular values. Then, we investigate the efficient use of Givens rotations as a vector rotation tool. The cancellation of cross-terms is presented as an efficient signal/noise separation technique which guarantees a better updating of the subspaces basis. Regarding the choice between inner and outer rotations, we properly use the permutation properties of Givens rotations to maintain the decreasing ordering of the singular values throughout the updating process and analyze the consequences on the tracking performance of QR Jacobi-type algorithms. Finally, based on the developed theory, we propose two efficient subspace tracking algorithms which outperform existing QR Jacobi-type algorithms. Comparative simulation experiments validate the concepts. ( 1999 Elsevier Science B.V. All rights reserved.