Proximity of Weighted and Layered Least Squares Solutions - Kitahara, Tomonari; Tsuchiya, Takashi (SIAM journal on matrix analysis and applications, 2009)
In this paper, the researchers analyze the limiting behavior of the weighted least squares problem ..., where each ... is a positive definite diagonal matrix. they consider the situation where the magnitude of the weights differs drastically from one block to the next so that ... Here max(...) and min(...) represent the maximum and minimum entries of diagonal elements, respectively. Specifically, they consider the case when the gap ... is very large or tends to infinity. Vavasis and Ye proved that the limiting solution exists (when the proportion of diagonal elements within each block ... is unchanged and only the gap g tends to ∞), and showed that the limit is characterized as the solution of a variant of the least squares problem called the layered least squares problem.(ProQuest: ... denotes formulae/symbols omitted.)