Indefinite QR Factorization

Let A be a Hermitian positive definite matrix given by its rectangular factor G such that A=G*G. It is well known that the Cholesky factorization of A is equivalent to the QR factorization of G. In this paper, an analogue of the QR factorization for Hermitian indefinite matrices is constructed. This problem has been considered by many authors, but the problem of zero diagonal elements has not been solved so far. Here we show how to overcome this difficulty.