A contribution to the conditioning theory of the indefinite least squares problems.

The conditioning theory of the indefinite least squares (ILS) problems is considered in the paper. Based on the well acknowledged fact that utilizing the intermediate results produced in the process of solving the problem can largely reduce the computational burden of computing the condition numbers, we employ two hyperbolic matrix decomposition based numerical algorithms to solve the ILS problems, and with its intermediate results the first order perturbation analysis and condition number theory of the ILS problems are fully investigated. The first order perturbation analysis gives a precise characterization of the matrix factors in influencing the forward errors. For the new explicit expressions of the condition numbers consisting of intermediate results, some compact forms or upper bounds are proposed to reduce its computational burden and storage requirement. Moreover, we also devise some efficient numerical algorithms to estimate the condition numbers by exploiting its special structures. Numerical experiments are given to illustrate the efficiency of our results. [ABSTRACT FROM AUTHOR]