A repository containing solutions to laboratory tasks for the 4th-semester Computational Methods course in Computer Science. Topics covered include Linear Systems, Floating Point Arithmetic, Singular Value Decomposition, Non-Linear Equations, Simulated Annealing, Search Engines, and Fast Fourier Transformation.
Some tasks are significantly larger and more detailed, often including reports and extensive documentation.
Using Gaussian Elimination & LU Decomposition to solve linear systems. Additionally, this lab includes solving an electric circuit (treated as a graph) by finding electric currents using Kirchhoff's and Ohm's Laws and reducing dependent equations.
Applying the Simulated Annealing metaheuristic to solve various optimization problems.
Building a search engine utilizing SVD, Cosine Similarity, and web crawling techniques.
Implementing Template Matching and Optical Character Recognition using Discrete Fourier Transformation and FFT.
These are smaller tasks, some of which may not be fully developed.
Exploring different approaches to summing numbers in computer arithmetic.
Approximating solutions to non-linear equations using the Bisection, Newton, and Secant methods.
Studying Singular Value Decomposition (SVD) techniques.
Exploring the Power and Reversed Power methods for spectral decomposition.
This format is structured to be more visually appealing and readable. Feel free to paste this updated version into your README file.