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In a system of equations with nine equations and nine unknown elements of the degree of three has been solved numerically with Mathematica software. In this method the roots are numerous, it is difficult to recognize the right roots.Can we solve these equations in a more confident way ?

Harry Peter
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anousheh
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    What do you mean with "the right roots"? – Florian Aug 30 '18 at 10:59
  • Thank you for your answer,the root that makes the equations zero. In general , how can a root be chosen from the roots obtained ? – anousheh Aug 30 '18 at 11:12
  • For a system of nonlinear equations you may get more than one solution, i.e., more than one set of roots where all equations are zero. This means there may not be one unique solution. In that case, all solutions are equally correct and there is no reason to favor one over the other. If you want to restore uniqueness you may need to pose additional constraints, motivated from your application. – Florian Aug 30 '18 at 11:25
  • The answer was very complete ,thank you.How to solve a system of (a large number of) nonlinear simultaneous equations using MATLAB? Which software is better than Matlab or Mathematica? – anousheh Sep 02 '18 at 07:53
  • I have a system of nine nonlinear equations with nine variables to solve in Mathematica.First I used Solve[sys,var] which did not work and also NSolve did not work and by the use of findroot, numerous roots are obtained. How can I make it work? Is there another way of solving this ? – anousheh Sep 02 '18 at 09:18
  • If findroot returns numerous roots then it seems to work fine. There will be numerous roots. Pick any of them, it doesn't matter which one. – Florian Sep 03 '18 at 14:56
  • @Florian- Thank you very much. – anousheh Sep 07 '18 at 19:26
  • Are we used in Matlab and mathematica by Newton - Raphson method to solve the system of nonlinear equations? In this way, is there a possibility of convergence problem in solving the equations? – anousheh Sep 25 '18 at 07:07
  • The numerous roots of the system of nonlinear equations can be explained due to the convergence problem in the solution? – anousheh Sep 25 '18 at 07:11
  • No, even without any convergence problems, there may be numerous solutions. One quadratic equation in one variable has two solutions. Two quadratic equations in two variables may easily have four solutions (see e.g. https://math.stackexchange.com/questions/2119007/how-do-you-solve-a-system-of-quadratic-equations). For degree three, you may already have three real solutions for one variable and one equation. Depending on how your equations line up it's no surprise this number shoots up for 9 variables in 9 equations. You can easily test it though: do all the roots you get satisfy all equations? – Florian Sep 26 '18 at 08:39
  • @ Florian Thank you. These equations have a set of positive roots and a set of negative root categories , how to limit the roots to a positive range in Mathematica ? – anousheh Sep 26 '18 at 16:11
  • These roots are dependent on a set of parameters that , by increasing these parameters , must increase their values , which in some cases the negative roots are increased and positive roots are decreased , and this is confusing in choosing the desired root – anousheh Sep 26 '18 at 16:12
  • These nonlinear algebraic equations are obtained by applying Galerkin method into a four - order partial differential equations, indicating that the roots of this equation represent the deflection of a steel plate , so we need only a set of root. – anousheh Sep 26 '18 at 16:31
  • I doubt the numerical solution of these equations by ordering of Findroot. If there is a method to resolve these nonlinear algebraic equations in another method, which ensures more accurate resolution , please give a guide me.Thank you for your kindness. – anousheh Sep 26 '18 at 16:38
  • How is the convergence problem possible ? And how does the problem emerge in the roots ? In various articles, this problem has been addressed in solving non - linear algebraic equations of the degree of three by the Newton - Raphson method. – anousheh Sep 26 '18 at 16:46
  • I suggest you specify your question and repost it at an appropriate site. For questions about Mathematica, you have a better chance of finding experts over at StackOverflow. You should try to be specific, it is not clear what you mean when you write "more accurate solution". As I told you many times, there may and will be numerous exact solutions to nonlinear equations. It doesn't get more accurate than that. How to find them is up to Mathematica or something for which you better ask for help somewhere else. Good luck! – Florian Sep 27 '18 at 08:19
  • I'm sorry for prolonging my questions,i received helpful comments from you .Thank you – anousheh Sep 28 '18 at 08:21
  • @Florian Hi, When the system of nonlinear algebraic equations is very large in size, when the Jacobian matrix is nearly singular or is severely ill-conditioned, What are the more robust methods for solving ill-conditioned problems nonlinear? – anousheh Nov 26 '18 at 05:46
  • I'd say you'll need some preconditioning but I'm definitely not an expert in numerics. Why not open a new question asking precisely that (with some more details like what's the size, what's the conditioning and what methods have you tried). – Florian Nov 26 '18 at 08:56
  • I opened the new question, but unfortunately I didn't get a response.Thank you for your patience in responding to me. – anousheh Nov 26 '18 at 14:58
  • Your question doesn't create any good incentive for providing an answer. I suggest you to read the entire thread of https://math.meta.stackexchange.com/questions/9959/how-to-ask-a-good-question#9960 and then try to improve your question-asking skills. – Florian Nov 26 '18 at 16:09
  • @Florian Thank you for your suggestion. – anousheh Nov 27 '18 at 16:01

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