Multivariate approximation of functions on irregular domains by weighted least-squares methods

Accurate Solution of Weighted Least Squares by Iterative Methods

We consider the weighted least-squares (WLS) problem with a very ill-conditioned weight matrix. Weighted least-squares problems arise in many applications including linear programming, electrical networks, boundary value problems, and structures. Because of roundoo errors, standard iterative methods for solving a WLS problem with ill-conditioned weights may not give the correct answer. Indeed, ...

Weighted total least squares formulated by standard least squares theory

This contribution presents a simple, attractive, and exible formulation for the weighted total least squares (WTLS) problem. It is simple because it is based on the well-known standard least squares theory; it is attractive because it allows one to directly use the existing body of knowledge of the least squares theory; and it is exible because it can be used to a broad eld of applications in t...

Least Squares Approximation by One-Pass Methods with Piecewise Polynomials

We propose several one-pass methods for data fitting in which a piecewise polynomial is used as an approximating function. The polynomial pieces are calculated step-by-step by the method of least squares as the data is -----------,scaIIIIed umy-once-from the begimring La tIre end. To calculate the least squares fitting in each step, we use three classes of data, namely: the data in the current ...

Weighted least squares method for the approximation of directional derivatives

Using the facet model we design a family of filters for the approximation of partial derivatives of the digital image surface. Prior information (e.g., local dominant orientation) are incorporated in a two dimensional weight function. A weighted least squares estimation of the facet parameters is applied in order to design the proposed filters. Exemplary application of the proposed filters to f...

Weighted least squares support vector machines: robustness and sparse approximation