A flexible condition number for weighted linear least squares problem and its statistical estimation

In this paper, we mainly focus on the derivation of a flexible condition number for weighted linear least squares problem and its estimation. With Fréchet derivative and Kronecker product, the explicit expression of the condition number is obtained. When the coefficient matrices are large and dense, considering the difficulties of explicitly forming the expression of condition number in computer, we also present its simplified form through a simple and easy to operate method. Two different condition estimation methods are introduced, and the numerical experiments are also performed to show the efficiency of the condition estimators.