davxy/numeric

Numerical Analysis algorithms in Python and Octave

Numerical Analysis

Companion book

Algorithms

Finite Arithmetic

• Machine precision computation
• Numerical cancellation example

Equation Roots

• Bisection method
• Newton-Raphson method
• Newton-Raphson with Aitken acceleration
• Quasi-Newton Chords method
• Quasi-Newton Secant method

Linear Algebra

• Reduced Row Echelon Form
• Diagonal systems
• Triangular systems
• LU factorization
• PA=LU factorization
• LL' Cholesky factorization

Polynomial Interpolation

• Lagrange interpolation polynomial
• Chebyshev nodes
• Divided differences
• Lebesgue function and constant grow
• Runge test
• Polynomial interpolation application: Toom-3 multiplication
• Cubic spline

Numerical differentiation

• Forward Finite differences (FFD)
• Symmetric differential quotient (SDQ)
• Condition number experiment: h threshold

Numerical integration

• Composite trapezoid method
• Composite Simpson's method
• Adaptive methods
• Romberg method

Misc

• Vandermonde matrix conditioning number graph

Dependencies

Python

• Python3
• NumPy (http://numpy.org)
• Matplotlib (https://matplotlib.org/)

Python3 and package manager system-wide installation

$ sudo apt install python3 pip3

Python3 packages installation (user only)

$ pip3 install numpy matplotlib

Octave

All in one octave package installation

$ sudo apt install octave