A problem from shape fitting is finding the sphere which has the least sum of squares fit to a set of points. Most current algorithms for this use an iterative process, with randomized restarting. We present, instead, two geometric transformations, and algorithms derived using them, which present alternate methods of solving the problem. We discuss running of these algorithms in three dimension...

Vector Fitting (VF) is an iterative technique to construct rational approximations based on multiple frequency domain samples, introduced by Gustavsen and Semlyen [1, 3]. VF is nowadays widely investigated and used in the Power Systems and Microwave Engineering communities. Numerical experiments show that VF has favorable convergence properties. However, so far, no theoretical proof for its con...

Data fitting is a fundamental tool in scientific research and engineering applications. Generally, there are two ingredients in solving data fitting problems. One is the fitting representation, and the other is the fitting method. Nowadays, the fitting of larger and larger quantities of data sets requires more compact fitting representation and faster fitting methods. The T-spline is a recently...

Beta is a widely used quantity in investment analysis. We review the common interpretations that are applied to beta in finance and show that the standard method of estimation – least squares regression – is inconsistent with these interpretations. We present the case for an alternative beta estimator which is more appropriate, as well as being easier to understand and to calculate. Unlike regr...

Here we describe a hierarchal and iterative data analysis algorithm used for searching, characterizing, and removing bright, monochromatic binaries from the Laser Interferometer Space Antenna (LISA) data streams. The algorithm uses the F -statistic to provide an initial solution for individual bright sources, followed by an iterative least squares fitting for all the bright sources. Using the a...

Recent work in testing and comparing maximum-inscribed, minimum-circumscribed, and minimum-zone (Chebyshev) fitting algorithms indicates that serious problems can exist in present commercial software packages. 1. Introduction The historical motivation for this work came as a result of the 1988 GIDEP alert [1] which warned of possible significant measurement uncertainty arising from least-square...

In this paper, an iterative method is proposed for solving matrix equation $sum_{j=1}^s A_jX_jB_j = E$. This method is based on the global least squares (GL-LSQR) method for solving the linear system of equations with the multiple right hand sides. For applying the GL-LSQR algorithm to solve the above matrix equation, a new linear operator, its adjoint and a new inner product are dened. It is p...

Fitting response surface models is usually carried out using statistical packages to solve complicated equations in order to produce the estimates of the model coefficients. This paper proposes a new procedure for fitting response surface models to mixed two-level and four-level factorial designs. New and easier formulae are suggested to calculate the linear, quadratic and the interaction coeff...

This work applies a least squares plane fitting (LSP) method as an alternative way of interpolating irregularly spaced pixel intensity values that are suitable for image reconstruction of a static scene via super-resolution (SR). SR is a term used within the computer vision and image processing community to describe the process of reconstructing a high resolution image from a sequence of severa...