Non-Linear and Simultaneous Equations

2021 ◽  
pp. 5-35
Author(s):  
Soumendra Nath Kuiry ◽  
Dhrubajyoti Sen
1976 ◽  
Vol 157 (2) ◽  
pp. 489-492 ◽  
Author(s):  
I A Nimmo ◽  
G L Atkins

1. Descriptions are given of two ways for fitting non-linear equations by least-squares criteria to experimental data. One depends on solving a set of non-linear simultaneous equations, and the other on Taylor's theorem. 2. It is shown that better parameter estimates result when an equation with two or more non-linear parameters is fitted to all the sets of data simultaneously than when it is fitted to each set in turn.


1958 ◽  
Vol 62 (572) ◽  
pp. 603-604 ◽  
Author(s):  
W. J. Goodey

The Calculation of the roots of an algebraic or transcendental equation in a single unknown is a problem of frequent occurrence. For a real root the usual procedure is to obtain a first approximation to the required quantity, graphically or otherwise, and to improve this approximation by successive applications of the Newton-Raphson process. The extension of this process to the improvement of an approximate solution of a set of non-linear simultaneous equations in n unknowns is fairly obvious, but it does not seem to have received much attention in text books, although the case of two unknowns is dealt with in Ref. 2.


2009 ◽  
Vol 88 (2) ◽  
pp. 151-160 ◽  
Author(s):  
Masato Yamada ◽  
Saburou Saitoh

2020 ◽  
Vol 9 (2) ◽  
pp. 263
Author(s):  
Pg. Mohammad Adib Ridaddudin Pg. Johari ◽  
Masitah Shahrill

The purpose of this study is to understand the causes of common errors and misconceptions in the learning attainment of simultaneous equations, specifically on linear and non-linear equations with two unknowns. The participants consisted of 30 Year 9 students in one of the elite government schools in Brunei Darussalam. Further analyses of their work led to the categorisation of four factors derived from the recurring patterns and occurrences. These four factors are complicating the subject, wrong substitution of the subject, mathematical error and irrational error in solving the question. These factors usually cause participants to make errors or simply misconceptions that usually led them to errors in solving simultaneous equations.


1967 ◽  
Vol 28 ◽  
pp. 105-176
Author(s):  
Robert F. Christy

(Ed. note: The custom in these Symposia has been to have a summary-introductory presentation which lasts about 1 to 1.5 hours, during which discussion from the floor is minor and usually directed at technical clarification. The remainder of the session is then devoted to discussion of the whole subject, oriented around the summary-introduction. The preceding session, I-A, at Nice, followed this pattern. Christy suggested that we might experiment in his presentation with a much more informal approach, allowing considerable discussion of the points raised in the summary-introduction during its presentation, with perhaps the entire morning spent in this way, reserving the afternoon session for discussion only. At Varenna, in the Fourth Symposium, several of the summaryintroductory papers presented from the astronomical viewpoint had been so full of concepts unfamiliar to a number of the aerodynamicists-physicists present, that a major part of the following discussion session had been devoted to simply clarifying concepts and then repeating a considerable amount of what had been summarized. So, always looking for alternatives which help to increase the understanding between the different disciplines by introducing clarification of concept as expeditiously as possible, we tried Christy's suggestion. Thus you will find the pattern of the following different from that in session I-A. I am much indebted to Christy for extensive collaboration in editing the resulting combined presentation and discussion. As always, however, I have taken upon myself the responsibility for the final editing, and so all shortcomings are on my head.)


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