Parallel Scaled Givens Rotations for the Solution of Linear Least Squares Problems.

Abstract : A class of parallel scaled Givens rotations, to be applied to weighted multiple linear least squares problems, is discussed. In comparison to Fast Givens transformations, properly scaled rotations for weighted problems exhibit the same stability, require fewer divisions, and avoid square roots as well as pivoting. Consequently, with a suitable elimination strategy, the algorithm is amenable to parallel linear-time implementation on systolic arrays in VLSI. Round off error and stability analyses are presented, indicating slightly less accumulation of round off error than known sequential methods. (Author)