ENUME_Projects

3 Projects in MATLAB regarding Numerical Methods problems.
Done during my 5th semester of studies, winter 2021.

1st Project

1. Write a program finding macheps in the MATLAB environment.
2. Write a general program solving a system of n linear equations Ax = b using Gaussian elimination with partial pivoting
3. Write a general program solving a system of n linear equations Ax = b using Gauss-Seidel and Jacobi iterative algorithms.
4. Write a program of the QR method for finding eigenvalues of 5x5 metrices:
   1. Without shifts
   2. With shifts calculated on the basis of an eigenvalue of the 2x2 right-lower-corner submatrix

2nd Project

1. Find all zeros of a function using:
   1. False position (regula falsi) method
   2. The Newton's method
2. Find all real and complex roots of a polynomial using Muller's method (using two versions). Compare the results
3. Find all real and complex roots of a polynomial using Laguerre's method. Compare the results

3rd Project

1. For a set of experimental measurements determine a polynomial function that best fits the experimental data, using least-squares approximation for different degrees.
2. Given a motion of a point by differential equations, determine the trajcetory of the motion on an interval with given initial conditions
   1. Using Runge-Kutta method of 4th order (RK4) and Adams Predictor-Corrector (P5EC5E)