Numerical methods written in Python 2.
Ordinary Differential Equations
- euler_method.py
- heun_method.py
- law_of_cooling.py
- ode12.py Adaptive ODE using Euler method and Heun's method
Matrix Algebra
- backward_substitution.py Solve a linear system given an upper triangular matrix
- forward_substitution.py Solve a linear system given an lower triangular matrix
- induced_matrix_norms.py Calculate p-induced matix norms
- householder_reflection_vis.py Visualizing householder reflection for QR Decomposition
- lu_decomposition.py LU decomposition
- qr_householder.py Householder reflection for QR decomposition
- qr_linear.py minimize || Ax - b || using qr factorization
- permutation_matrix.py How to swap columns and ows using permutation matrices
Rootfinding Methods
- rootfinding_methods.py Bisection, fixed-point, Newton, and Secant methods
- vector_newton.py
- eigenvalue_polynomials.py Eigenvalue method to find roots of polymonials
Eigenvalues, Eigenvectors, and SVD
Iterative Methods for Ax=b
- jacobi_iterative_form.py Jacobi Iterative Method
- jacobi_matrix_form.py Jacobi Matrix Method
- gauss-seidel_iterative_form.py Gauss-Seidel Iterative Method
- gauss-seidel_matrix_form.py Gauss-Seidel Matrix Method
Signal Processing and Fourier Transform
- time_shift_fourier.py Cross Correlation in the frequency domain
- cross_correlation.py Brute-Force Cross Correlation
- derivative_fourier.py 1st order derivative approximation using Fourier Transform
- dft.py 1D Discrete Fourier Transform
- dft2.py 2D Discrete Fourier Transform
- dft_inverse.py 1D Inverse Discrete Fourier Transform
- dft2_inverse.py 2D Inverse Discrete Fourier Transform