Total least-squares (TLS) adjustment is used to estimate the parameters in the errors-in-variables (EIV) model. However, its exact solution is rather complicated, and the accuracies of estimated parameters are too difficult to analytically compute. Since the EIV model is essentially a non-linear model, it can be solved according to the theory of non-linear least-squares adjustment. In this cont...

Methods are developed for the design of electrical impedance tomographic reconstruction algorithms with specified properties. Assuming a starting model with constant conductivity or some other specified background distribution, an algorithm with the following properties is found. (1) The optimum constant for the starting model is determined automatically. (2) The weighted least-squares error be...

This article deals with estimation of the change-point in a sequence of independent random variables. It is based on a least squares process endowed with a weight function. For finite sample sizes we derive bounds of the error probability. They immediately yield rates of consistency which are known to be optimal. Our findings extend and sharpen earlier results of Antoch, Hušková and Veraverbeke...

Iteratively Re-weighted Least Squares (IRLS) is a method for solving minimization problems involving non-quadratic cost functions, perhaps non-convex and non-smooth, which however can be described as the infimum over a family of quadratic functions. This transformation suggests an algorithmic scheme that solves a sequence of quadratic problems to be tackled efficiently by tools of numerical lin...

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, ...

This paper presents a generalization of the "weighted least-squares" (WLS), named "weighted pairing least-squares" (WPLS), which uses a rectangular weight matrix and is suitable for data alignment problems. Two fast solving methods, suitable for solving full rank systems as well as rank deficient systems, are studied. Computational experiments clearly show that the best method, in terms of spee...

In recent years most research into lossless and near lossless compression of greyscale images could be characterized as belonging to either of two distinct groups The rst group which is concerned with so called practical algorithms encom passes research into methods that allow compression and decompression with low to moderate computational complexity while still obtaining impressive compressio...

The behavior of estimators for misspecified parametric models has been well studied. We consider estimators for misspecified nonlinear regression models, with error and covariates possibly dependent. These models are described by specifying a parametric model for the conditional expectation of the response given the covariates. This is a parametric family of conditional constraints, which makes...