Abstract: A new kind of weighted generalized inverse was defined to study indefinite
least squares (ILS) problem and equality constrained indefinite least squares (ILSE)
problem. By applying hyperbolic-QR factorization, the solutions to the two problems were
obtained. Also the perturbation bounds of the solutions were derived.

Key words: indefinite least squares problem, equality constrained indefinite least squares problem, weighted generalized inverse , perturbation analysis, indefinite least squares problem, equality constrained indefinite least squares problem, weighted generalized inverse