The hyperbolic singular value decomposition and applications

A new generalization of singular value decomposition (SVD), the hyperbolic SVD, is advanced, and its existence is established under mild restrictions. Two algorithms for effecting this decomposition are discussed. The new decomposition has applications in downdating in problems where the solution depends on the eigenstructure of the normal equations and in the covariance differencing algorithm for bearing estimation in sensor arrays. Numerical examples demonstrate that, like its conventional counterpart, the hyperbolic SVD exhibits superior numerical behavior relative to explicit formation and solution of the normal equations. (However, unlike ordinary SVD, it is applicable to eigenanalysis of covariances arising from a difference of outer products)