Rounding-error and perturbation bounds for the indefinite QR factorization (Q1976912)

Indefinite QR factorization is a generalization of the usual 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 authors present rounding-error and perturbation bounds for the so-called ``triangular'' case of the indefinite QR factorization. It is pointed out that these bounds fit well into the relative perturbation theory for Hermitian matrices given in factorized form.