Using Dual Techniques To Derive Error Analysis Of A Linear Function Of A Weighted Least Squares Solution And Residual

In this thesis, based on dual techniques, we define condition numbers for linear func-tionals of the solution and residual of weighted linear least squares problem. The explicit expressions are derived, which can be easily computed when the dimension of linear functional is low due to dual operator theory. Moreover, we use augmented system to get componentwise perturbation analysis for the solution and residual of weighted linear least squares problems. Numerical examples show that our condition numbers can give sharp perturbation bounds and reveal the true conditioning of the problem.