Numerical Analysis Blog

Weeks 4-7

March, 26, 2021 by Instructor

The material covered these weeks may be structured as follows:

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Lectures (Cursuri 4-7)

1. Metode iterative pentru rezolvarea ecuațiilor neliniare.
2. Metode numerice de rezolvare a ecuațiilor diferențiale. Metode explicite vs metode implicite.
3. Interpolare polinomiala (Lagrange, Hermite), diferente divizate.
4. Interpolare spline (spline liniar, spline-uri cubice)

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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.
7. Numerical methods for ODEs. Convergence and stability.
8. Divided differences and polynomial interpolation.
9. Spline interpolation: linear and cubic.