Numerical investigations of linear least squares methods for derivative estimation

Nonparametric Least Squares Estimation in Derivative Families

Cost function estimation often involves data on a function and a family of its derivatives. It is known that by using such data the convergence rates of nonparametric estimators can be substantially improved. In this paper we propose series-type estimators which incorporate various derivative data into a single, weighted, nonparametric, least-squares procedure. Convergence rates are obtained, w...

Numerical methods for generalized least squares problems

Usually generalized least squares problems are solved by transforming them into regular least squares problems which can then be solved by well-known numerical methods. However, this approach is not very effective in some cases and, besides, is very expensive for large scale problems. In 1979, Paige suggested another approach which consists of solving an equivalent equality-constrained least sq...

Least-Squares Methods for Linear Elasticity

This paper develops least-squares methods for the solution of linear elastic problems in both two and three dimensions. Our main approach is defined by simply applying the L2 norm least-squares principle to a stress-displacement system: the constitutive and the equilibrium equations. It is shown that the homogeneous least-squares functional is elliptic and continuous in the H(div; Ω)d × H1(Ω)d ...

Decomposition Methods for Least Squares Parameter Estimation

In this paper least squares method with matrix decomposition is revisited and a multiple model formulation is proposed The proposed formulation takes advantage of the well established decomposition methods but possesses a multiple model structure which leads to simpler and more exible implementations and produces more infor mation than the original least squares methods Several application exam...

An Estimation Of Seasonal GDP Gap In Iran: Application Of Adaptive Least Squares Methods