2013/05/27 by Benjamin Lenoir
Engineering · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Computer science #Equivalence (formal languages) #Estimator #Generalized least squares #Least-squares function approximation #Mathematical optimization #Mathematics #Non-linear least squares #Scientific Research and Discoveries #Statistical and numerical algorithms #Statistics #Structural Health Monitoring Techniques #Total least squares #math.OC #stat.ME
paper · pdf · doi:10.1007/s11081-013-9217-7
published as Optimization and Engineering 15:3 (2014) 609-617 · 7 pages
arxiv created 2013/05/27 · openalex publication_date 2013/06/15 · arxiv updated 2015/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The least squares method allows fitting parameters of a mathematical model from experimental data. This article proposes a general approach of this method. After introducing the method and giving a formal definition, the transitivity of the method as well as numerical considerations are discussed. Then two particular cases are considered: the usual least squares method and the Generalized Least Squares method. In both cases, the estimator and its variance are characterized in the time domain and in the Fourier domain. Finally, the equivalence of the Generalized Least Squares method and the optimal filtering technique using a matched filter is established.