Rounding-error and perturbation bounds for the indefinite QR factorization Original Research Article

Indefinite QR factorization is a generalization of the well-known QR factorization, where Q is a unitary matrix with respect to the given indefinite inner product matrix J. This factorization can be used for accurate computation of eigenvalues of the Hermitian matrix A=G*JG, where G and J are initially given or naturally formed from initial data. The classical example of such a matrix is A=B*B−C*C, with given B and C. In this paper we present the rounding-error and perturbation bounds for the so called “triangular” case of the indefinite QR factorization. These bounds fit well into the relative perturbation theory for Hermitian matrices given in factorized form.