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# In modeling and optimization of real processes often occurs the pro...

In modeling and optimization of real processes often occurs the problem of solving systems of nonlinear equations (SNE).

For solving SNE generally use iterative methods. There are considered two of the most common iterative methods: Newton’s method and its modification.

Methods were compared by the following characteristics: the conditions of application methods; conditions of convergence and rate of convergence; the amount of computing to achieve the desired accuracy of the approximate solution.

The developed program (in C # language) implements algorithms of these two iterative methods.

Comparison of methods carried out on particular examples. Examples consist of a systems of two nonlinear equations given initial approximation and precision. Each example was resolved in the program and manually.

In addition to the basic comparison of Newton's method and its modifications carried out analysis of single stage and two-stage methods.

For solving SNE generally use iterative methods. There are considered two of the most common iterative methods: Newton’s method and its modification.

Methods were compared by the following characteristics: the conditions of application methods; conditions of convergence and rate of convergence; the amount of computing to achieve the desired accuracy of the approximate solution.

The developed program (in C # language) implements algorithms of these two iterative methods.

Comparison of methods carried out on particular examples. Examples consist of a systems of two nonlinear equations given initial approximation and precision. Each example was resolved in the program and manually.

In addition to the basic comparison of Newton's method and its modifications carried out analysis of single stage and two-stage methods.

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In the modeling and optimization of real-life processes, the problem of solving systems of nonlinear equations (SNE) often occurs.

SNE are generally solved using iterative methods.

The two most common iterative methods are considered to be Newton’s method and its extension.

Methods were compared according to the following characteristics: the conditions of application methods; conditions of convergence and rate of convergence; the number of iterations required to achieve the desired accuracy of the approximate solution.

I'm not sure of "the conditions of application methods", so I haven't suggested any changes.

The program, which was developed in C#, implements algorithms using both these iterative methods.

Comparison of the methods carried out on particular examples.

The examples consist of a system of two nonlinear equations, with a given initial approximation and precision.

Each example was resolved both using the program and manually.

In addition to the basic comparison of Newton's method and its modifications, we carried out an analysis by single stage and two-stage methods.

I'm not sure exactly what you did, so my changes, although grammatically correct, might say something different from what you mean.

In the last sentence:

In addition to the basic comparison of Newton's method and its modifications, we carried out an analysis by single stage and two-stage methods.

I can't use words "I" and "we". The work should be impersonal.

So can I change it this way?

In addition to the basic comparison of Newton's method and its modifications, WAS carried out an analysis by single stage and two-stage methods.

"was" cannot be used like this. It must have a subject.

Can you use "the team" instead of "we"?

Or you can make the analysis the subject.

In addition to the basic comparison of Newton's method and its modifications, an analysis WAS CARRIED OUT by single stage and two-stage methods.

I agree that it's outdated and silly :c