Reducing the Computations of the Singular Value Decomposition Array Given by Brent and Luk
Bo Yang, J.F. Böhme · SIAM Journal on Matrix Analysis and Applications · 1991
A new, efficient, two-plane rotation (TPR) method for computing two-sided rotations involved in singular value decomposition (SVD) is presented. It is shown that a two-sided rotation can be evaluated by only two plane rotations and a few additions. This leads to significantly reduced computations. Moreover, if coordinate rotation digital computer (CORDIC) processors are used for realizing the processing elements (PEs ) of the SVD array given by Brent and Luk, the computational overhead of the diagonal PEs due to angle calculations can be avoided. The resulting SVD array has a homogeneous structure with identical diagonal and off-diagonal PEs. Similar results can also be obtained if the TPR method is applied to Luk’s triangular SVD array and to Stewart’s Schur decomposition array.