Unifying Least Squares, Total Least Squares and Data Least Squares

Abstract

The standard approaches to solving overdetermined linear systems A x ≈ b construct minimal corrections to the vector b and/or the matrix A such that the corrected system is compatible. In ordinary least squares (LS) the correction is restricted to b, while in data least squares (DLS) it is restricted to A. In scaled total least squares (Scaled TLS) [15], corrections to both b and A are allowed, and their relative sizes depend on a parameter γ. Scaled TLS becomes total least squares (TLS) when γ = 1, and in the limit corresponds to LS when γ → 0, and DLS when γ → ∞.