Fitting of experimental data with a polynomial determined by Gaussian least-squares analysis is a common and well-established praxis. However, there seems to be a lack in consistency if the resulting fit parameters are to be interpreted as physically meaningful quantities. Therefore, a detailed investigation of the fitting procedure itself as well as of the measuring process, including possible...

Optical power spectra obtained from experiments or from numerical simulations are probabilistic in nature. When fitting such spectra to few-parameter analytical line shapes, the results from a weighted nonlinear least squares fit are significantly better than those from an unweighted fit. This is demonstrated by fitting a Lorentzian to directly simulated power spectra and to power spectra obtai...

There are thousands of articles published on variants of splines, including least squares cubic splines. One of the first least squares articles was de Boor and Rice [1], and a comprehensive explanatory textbook is Dierckx [2]. Unfortunately, every example in the literature and on the web of a least squares cubic spline makes use of B-splines. While B-splines have a certain elegance, they are s...

Vector Fitting is a popular method of constructing rational approximants designed to fit given frequency response measurements. The original method, which we refer to as VF, is based on a least-squares fit to the measurements by a rational function, using an iterative reallocation of the poles of the approximant. We show that one can improve the performance of VF significantly, by using a parti...

It has recently been widely argued that all consciousness is perceptual, including the conscious experience of action. This paper argues that there can be a conscious component of the experience of action that is not perceptual. The argument is based on Searle’s concept of “direction of fit” and the conditions of satisfaction of an intention. The conditions of satisfaction of an intention diffe...

February 19, 2015 Version 1.4.7 Date 2013-03-04 Author Peter Frommolt Maintainer Peter Frommolt Title Inferences for biand trifactorial trial designs Depends mvtnorm,multcomp,lattice,graphics,methods,Rcpp (>= 0.8.8) LinkingTo Rcpp Description This package makes global and multiple inferences for given biand trifactorial clinical trial designs using bootstrap method...

This paper addresses a problem arising in the reverse engineering of solid models from depth-maps. We wish to identify and fit surfaces of known type wherever these are a good fit. This paper presents a set of methods for the least-squares fitting of spheres, cylinders, cones and tori to three-dimensional point data. Least-squares fitting of surfaces other planes, even of simple geometric type,...

on the xy-plane are bounded regions, called bases of digital plane segments. So, if the plane a is digitized and if a In this paper we prove that digital plane segments and their least-squares plane fit are in one-to-one correspondence, which region Q in the xy-plane is given, then the digital plane gives a simple representation of a digital plane segment by its segment P(a, Q) (more precisely,...