Computational Methods
Tasks from "Computational Methods in Science and Technology" course at AGH University. Written in Python.
Lab 2 - Interpolation
- Chebyshev nodes
- spline functions
Lab 3 - Singular Value Decomposition 1
- the axis of the ellipsoids
- low rank approximation used for image compression
Lab 4 - Singular Value Decomposition 2
- word frequency search engine
- bag of words with words frequency in text
- term by document matrix with bags of words
- IDF
- removing noise with SVD and low rank approximation
Lab 5 - Nonlinear equations
- finding roots of nonlinear equations
- bisection
- Newton's method
- secant method
Lab 6 - Solving systems of linear equations (and electric circuit analysis)
- Gauss-Jordan's method
- LU matrix factorization
- electric circuit analysis
- finding current value
- using Kirchoff's Laws
- using method of nodal potentials
- finding current value
Lab 7 - Spectral Decomposition
- power method
- inverse power method
Lab 8 - Page Rank
- simple vertex ranking
- Page Rank
Lab 9 - QR Decomposition
- Gram-Schmidt's method
- solving systems of linear equations using QR method
Lab 10 - Discreet Fourier Transformation
- DFT
- IDFT
- FFT (Cooleya-Turkey's alghoritm)
- signals transformation
Lab 11 - Random number generators
- test of Mersenne Twister and PCG64 generators
- random number generator (from normal distribution) using Boks-Muller's method
- Monte Carlo's method
Lab 12 - Differential equations
- Runge-Kuta method
- adaptive Runge-Kutta-Fehlberg method
Lab 12 - Minimalisation
- the traveling salesman problem