The goal of this project is to program algorithms dedicated to the research of roots of systems of non-linear equations. The method promoted here is the Newton-Raphson algorithm, and the goal is to evaluate the assets and liabilities of such a solution. This shall be done by testing the method in different settings. In the following, you will be proposed a list of applications where this algorithm is necessary. You must program at least two of these applications, and then write a summary of your experiments as a conclusion. More applications are not synomyms of better work.
This project covers a number of algorithms and programming techniques that are not directly addressed in the course. We advise you to be autonomous by making the most of your own knowledge and the documents available. The teacher will not answer the questions that he feels you can answer on your own.
The project is made of:
Conclude your experimentations by an analysis of the problems encountered and the benefits of using an algorithm such as the Newton-Raphson.
The comparison shall be based on the results investigated in the course, and possibly the reading of the chapter 9 of the Numerical Recipes, available at this location (chap. 9, Root Finding and Nonlinear Sets of Equations).
Even if the subject is in english, the project should be done in french.