Numerical Analysis Blog

This week's material

October 15, 2017 by Instructor

The material covered this week may be structured as follows:

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Lecture 3 (Curs 3)

1. Numerical solutions to nonlinear equations (Rezolvarea numerică a ecuațiilor neliniare): $\begin{array}{cc}& f\left(x\right)=0,f:ℝ\to ℝ.\hfill \end{array}$ We discuss a general approach based on rewriting the above equation in the form: $\begin{array}{cc}& x=g\left(x\right),\hfill \end{array}$ based on which we can construct an iterative method.
2. The bisection method (metoda injumatatirii). Algoritm si convergenta.
3. Newton's method (metoda lui Newton sau metoda tangentei). Derivation of the method, algorithm and convergence.
4. Quasi-Newton methods: the secant method (metoda secantei).

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Laboratory (Laborator).

1. Iterative methods for linear systems: implementation of Jacobi, Gauss-Seidel and SOR methods (if these were not implemented before).
2. Linear regression and the least squares method (Regresie liniară și metoda celor mai mici pătrate)).
3. Implementation of the bisection method. Matching the theoretical results with the experimental ones.
4. Implementation of Newton's method. Convergence analysis.
5. Newton's method for nonlinear systems. Implementation and convergence analysis.
6. The secant method for nonlinear equations. Implementation and convergence analysis.