The hyperbolic elimination method for solving the equality constrained indefinite least squares problem

Recently, Liu and Wang [Q. Liu and M. Wang, Algebraic properties and perturbation results for the indefinite least squares problem with equality constraints, Int. J. Comp. Math. 87(2) (2010), pp. 425-434.] proved that the solution of the equality constrained indefinite least squares (ILSE) problem min Bx=d(b-Ax)TJ(b-Ax), J=diag(-Iq, Ip) is the limit of the solution of the unconstrained weighted indefinite least squares (WILS) problem [image omitted] and J<SU similar to</SU=diag(Is, J) as the weight tends to infinity, assuming that B has full row rank and xTATJAx0 for all nonzero xnull (B). Based on this observation, we derive a type of elimination method by applying the hyperbolic QR factorization method to above WILS problem and taking the limit analytically. Theoretical analysis shows that the method obtained is forward stable under a reasonable assumption. We illustrate our results with numerical tests.