On The Condition Number And Backward Error Analysis For Indefinite Linear Least Squares Problems

In this thesis, we study the backward error and condition number of the indefinite least squares problem. Using dual techinics of condition number theory, we derive the explicit expressions of the mixed and componetnwise condition numbers for the indefinite least squares problem. Hyperbolic QR decomposition is one of the direct methods for solving the indefinite least squares problem. Using hyperbolic QR decomposition, we can rewire the derived condition number expressions in a more compact form, which can be used to compute the corresponding condition numbers with low computational complexity.For the normise backward error of the indefinite least square problem and the equality constrained indefinite least square problem, we adopt the linearization method to derive the tight estimations for the exact backward normwise errors.The numerical examples show that the derived condition numbers can give sharp perturbation bound with respect to the interested component of the solution. And the linearization estimations are effective for the normwise backward errors.