Numerical Methods

This repository contains lab exercises from a Numerical Methods course I completed during my 4th semester. The labs cover a wide range of numerical techniques and algorithms, as outlined below.

Topics Covered

1. Direct Methods for Solving Systems of Linear Equations
2. LU Decomposition and Matrix Inversion
3. Iterative Methods for Solving Systems of Linear Equations using Jacobi's Method
4. Diagonalization of the Energy Operator Matrix in 2D
5. Eigenvalue and Eigenvector Determination for Symmetric Matrices using the Power Method with Hotelling's Reduction
6. Root Finding for Polynomials using the Iterative Division Method (Newton's Method)
7. Lagrange Interpolation with Optimization of Node Positions
8. Spline Interpolation through Second Derivative Values at Nodes
9. Approximation in the Basis of Gram Polynomials
10. Function Minimization using Simulated Annealing
11. Signal Denoising using FFT - Convolution of Functions
12. Richardson Extrapolation for Integration using Simpson's and Milne's Formulas
13. Estimating Improper Integrals using Gaussian Quadrature
14. Generating Pseudo-Random Number Sequences with a Normal Distribution using the Elimination Method