A weighted-norm least-squares method is considered for the numerical approximation of solutions that have singularities at the boundary. While many methods suffer from a global loss of accuracy due to boundary singularities, the least-squares method can be particularly sensitive to a loss of regularity. The method we describe here requires only a rough lower bound on the power of the singularit...

vii List of Figures x List of Tables xi I Direct Minimization of the Equation Residuals 1

In this paper we address the numerical solution of minimal norm residuals of nonlinear equations in finite dimensions. We take particularly inspiration from the problem of finding a sparse vector solution of phase retrieval problems by using greedy algorithms based on iterative residual minimizations in the `p-norm, for 1 ≤ p ≤ 2. Due to the mild smoothness of the problem, especially for p→ 1, ...

A space-time Galerkin/least-squares finite element method was presented in [l] for numerical simulation of single-carrier hydrodynamic semiconductor device equations. The single-carrier hydrodynamic device equations were shown to resemble the ideal gas equations and Galerkin/least-squares finite element method, originally developed for computational fluid dynamics equations [16], was extended t...

In this work we review the opportunities given by the use of local maximumentropy approximants (LME) for the simulation of forming processes. This approximation can be considered as a meshless approximation scheme, and thus presents some appealing features for the numerical simulation of forming processes in a Galerkin framework. Especially the behavior of these shape functions at the boundary ...

Composite load model is developed for 1-24 hours ahead prediction of hourly electric loads. The load model is composed of three components : the nominal load, the type load and the residual load. The nominal load is modeled such that the Kalman filter can be used and the parameters of the model are adapted by the exponentially weighted recursive least squares method. The type load component is ...

The Þnite sample behaviour is analysed of particular least squares (LS) and a range of (generalized) method of moments (MM) estimators in panel data models with individual effects and both a lagged dependent variable regressor and another explanatory variable. The latter may be affected by lagged feedbacks from the dependent variable too. Asymptotic expansions indicate how the order of magnitud...

Least squares methods are effective for solving systems of partial differential equations. In the case of nonlinear systems the equations are usually linearized by a Newton iteration or successive substitution method, and then treated as a linear least squares problem. We show that it is often advantageous to form a sum of squared residuals first, and then compute a zero of the gradient with a ...