Arithmetic implementation of the Givens QR triarray

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Abstract
For fast and numerically stable algorithms, array processors with floating point multiplication, division, and square rooting are necessary. The authors consider the use of the arithmetic operation of square rooting in the QR algorithm as used in many linear algebraic signal processing algorithms. Rather than reformulating the algorithms to be square root free with the inherent problems of numerical instability, loss of orthogonality, and overflow/underflow, the square root is reconsidered from first principles and arrays are designed that are as fast and have a smaller chip area than the analogous division arrays. This implies that implementations such as square foot free Givens rotations should not be considered in an application-specific integrated circuit or similar design due to their potential instability and susceptibility to overflow.<>