Rounding-error and perturbation bounds for the indefinite QR factorization

S Singer - Linear algebra and its applications, 2000 - elibrary.ru
Linear algebra and its applications, 2000elibrary.ru
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* BC* 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 …
Аннотация
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* BC* 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.
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