3 Projects in MATLAB regarding Numerical Methods problems.
Done during my 5th semester of studies, winter 2021.
- Write a program finding macheps in the MATLAB environment.
- Write a general program solving a system of n linear equations Ax = b using Gaussian elimination with partial pivoting
- Write a general program solving a system of n linear equations Ax = b using Gauss-Seidel and Jacobi iterative algorithms.
- Write a program of the QR method for finding eigenvalues of 5x5 metrices:
- Without shifts
- With shifts calculated on the basis of an eigenvalue of the 2x2 right-lower-corner submatrix
- Find all zeros of a function using:
- False position (regula falsi) method
- The Newton's method
- Find all real and complex roots of a polynomial using Muller's method (using two versions). Compare the results
- Find all real and complex roots of a polynomial using Laguerre's method. Compare the results
- For a set of experimental measurements determine a polynomial function that best fits the experimental data, using least-squares approximation for different degrees.
- Given a motion of a point by differential equations, determine the trajcetory of the motion on an interval with given initial conditions
- Using Runge-Kutta method of 4th order (RK4) and Adams Predictor-Corrector (P5EC5E)