An on-line CORDIC implementation for computing the Generalized Singular Value Decomposition is presented. Among several algorithms, the implementation shown is based on Luk's parallel version for a triangular processor array, using odd-even ordering. To implement GSVD, the CORDIC approach is attractive compared with using conventional arithmetic units, such as square root, divider and multiplier. However, the CORDIC module is relatively slow because of the requirement of full precision computation to determine the direction of the angle and the variable shifter in the basic step. To avoid this, the use of redundant and on-line CORDIC has been proposed previously for SVD and matrix triangularization. This results in a significant speedup at some additional cost because of the variable scaling factor introduced. The extension of on-line CORDIC approach to the GSVD is presented. The advantages of this approach are more significant in GSVD because of the longer sequence of dependent operations. This makes the combination of the short step time of on-line CORDIC and the overlapping capability of on-line very attractive. By comparing it with conventional approach as well as CORDIC approach with full precision computation, we show that a speedup of about 5 can be achieved.
"On-Line CORDIC For Generalized Singular Value Decomposition(GSVD)", Proc. SPIE 1058, High Speed Computing II, (17 May 1989); doi: 10.1117/12.951687; https://doi.org/10.1117/12.951687