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numerical_algorithm

This repo contains a few numerical algorithms I wrote during one of my engineering classes. The files names and associated information is summarised below.

numerical_integration

  1. Pick a function to integrate and define in integral().
  2. Pick bounds of integration and specify the exact answer in true_value.
  3. Select a range of increments for discrete calculations, specify in delta_x.
  4. Modify x_coordinates if needed, to match the delta_x.

Example plot shown below:

image

cholesky_dcomp

A method to factorise a squre matrix in Lower and Upper triangle matrices (LU decomposition). This only works for Hermitian, positive definite matrix. Refer https://byjus.com/maths/cholesky-factorization/ for more information.

matrix_solver

This file contains 2 main functions:

  1. calculate the determinant of any matrix
  2. solve sparse tri-diagonal matrix (refer: https://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm)