/Computational-Methods

Tasks from "Computational Methods in Science and Technology" course at AGH University.

Primary LanguageJupyter Notebook

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

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