Journal ArticleDOI
The Modified Gauss-Newton Method for the Fitting of Non-Linear Regression Functions by Least Squares
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TLDR
The experimental scientist is frequently faced with the task of determining the functional relation between a response, y and a number of inputs, x, x2,. * *, x, with the help of empirical data.Abstract:
The experimental scientist is frequently faced with the task of determining the functional relation between a 'response', y and a number of 'inputs', x , x2, . * * , x, with the help of empirical data. Often the mathematical form of the functional relation is assumed to be known and is written in the form of a 'regression function',read more
Citations
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Journal ArticleDOI
Application of the maximum likelihood principle to separate exponential terms in T2 relaxation of nuclear magnetic resonance
TL;DR: The results from tissue measurements demonstrate that the method is effective even in cases where graphical peeling would clearly not yield reliable results, and the comparison to non-linear least squares analysis showed that the maximum likelihood method is generally superior in estimating the parameters in difficult cases.
Journal ArticleDOI
The non-linear least-squares of condition equations
TL;DR: In this article, the author constructs general algorithms for the non-linear least squares of condition equations and shows the procedure of their application for the settlement of the problem of unfavorable condition equations in the adjustment of a quadrilateral.
Journal ArticleDOI
A Model-Based Hybrid Ultrasonic Gas Flowmeter
TL;DR: In this paper, a hybrid dual-path ultrasonic sensor is designed to make full use of the advantages of the two modes, combining the transmission "Z" mode and the reflection "V" mode, a new model-based hybrid ultrasonic gas flowmeter is developed.
Book ChapterDOI
Gradient methods for the optimization of dynamic* system parameters by hybrid computation
George A. Bekey,Robert B. McGhee +1 more
TL;DR: This chapter discusses the computer implementation of both continuous and discrete gradient methods for adjusting the parameters of a dynamic system so as to match a specified response function as closely as possible.
Journal ArticleDOI
Characterization of grain boundaries in polycrystalline solar cells using a computerized electron beam induced current system
C. Donolato,R. O. Bell +1 more
TL;DR: In this paper, the automatic evaluation of grain boundary activity in polycrystalline solar cells is carried out by interfacing a microcomputer to a scanning electron microscope operating in the electron beam induced current mode (EBIC).
References
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Journal ArticleDOI
A method for the solution of certain non – linear problems in least squares
TL;DR: In this article, the problem of least square problems with non-linear normal equations is solved by an extension of the standard method which insures improvement of the initial solution, which can also be considered an extension to Newton's method.
Book ChapterDOI
On the Experimental Attainment of Optimum Conditions
George E. P. Box,K. B. Wilson +1 more
TL;DR: The work described in this article is the result of a study extending over the past few years by a chemist and a statistician, which has come about mainly in answer to problems of determining optimum conditions in chemical investigations, but they believe that the methods will be of value in other fields where experimentation is sequential and the error fairly small.