A rotation based method for solving covariance and related linear systems

An effective algorithm is presented for the Cholesky factorization of symmetric linear system equations with low displacement ranks. This proposed method represents an improved implementation of the generalized Schur algorithm (GSA) proposed by T. Kailath et al. (1979). It is shown that the (GSA) can be implemented with a sequence of circular and hyperbolic plane rotations. With careful arrangement, the number of the numerically undesirable hyperbolic rotations can be reduced to one per iteration. Hence the numerical stability of its algorithm is significantly improved. It is also shown that the GSA can be generalized to handle indefinite low-displacement rank liner systems as well. This improvement expands the potential applications of GSA for practical problems