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In this paper, based on the theory of adjoint operators and dual norms, wedefine condition numbers for a linear solution function of the weighted linearleast squares problem. The explicit expressions of the normwise andcomponentwise condition numbers derived in this paper can be computed at lowcost when the dimension of the linear function is low due to dual operatortheory. Moreover, we use the augmented system to perform a componentwiseperturbation analysis of the solution and residual of the weighted linear leastsquares problems. We also propose two efficient condition number estimators.Our numerical experiments demonstrate that our condition numbers give accurateperturbation bounds and can reveal the conditioning of individual components ofthe solution. Our condition number estimators are accurate as well asefficient.

A Condition Analysis of the Weighted Linear Least Squares Problem Using Dual Norms