Stabilized hyperbolic Householder transformations

A modification of the hyperbolic Householder scheme is introduced which is demonstrably stable theoretically (according to an established stability criterion) and which exhibits superior numerical behavior in simulations. The modified transform scheme effects downdating by applying conventional orthonormal, rather than hyperbolic, Householder transformations to the data. The latter have preferable numerical properties. However, the construction of these orthonormal operators itself requires hyperbolic computations. Thus, the proposed method is, in some sense, half hyperbolic and half orthonormal. There is no computational penalty incurred with these stabilized hyperbolic Householder transforms; they enjoy an operation count identical to their conventional counterparts.<>