Recursive Givens reduction using a second-order window

A new form of the recursive Givens reduction (the array of W.M. Gentleman and H.T. Kung, 1981) is discussed. The new algorithm uses a modified Barnwell window in contrast to the classical solution which relies on a simple exponential decay. The modified Barnwell window has much better spectral properties when compared to the exponential window, and hence the new algorithm exhibits a considerably improved steady-state and tracking behavior. It is shown that the recursive Givens reduction based on the modified Barnwell window can be implemented with two conventional exponentially weighted systolic arrays of the Gentleman and Kung type which are operated in parallel with little intermediate processing