teaching:methcalchim:system_of_linear_equations

Ceci est une ancienne révision du document !

# System of linear equations

Numerical methods used to solve such problem allow to introduce and experiment on Time_complexity, considering cubic time behavior of standard algorithms and i.e. quadratic time solutions using LU decomposition.
• Gaussian_elimination, Gauss and Gauss-Jordan eliminations (diagonalization, triangularization)
• Pivot_element, pivoting
• Chapter 2 in the book “Numerical Recipes” :
• 2.0 Introduction
• 2.1 Gauss-Jordan Elimination
• 2.2 Gaussian Elimination with Backsubstitution
• 2.3 LU Decomposition and Its Application
• Python NumPy library : NumPy Reference
• Time complexity analysis
• Hint : in Python, use the timeit module
• Exercices :
• write a python function for diagonalisation with partial pivoting
• random numbers → linear systems
• comparison with numpy standard library
• measurements of execution time to check cubic complexity
• Thermal diffusion and chemical diffusion (transient or stationary) on a regular 1D space with equidistant steps. ODE equations can be writen such a given evolution equation for node # i only imlies nodes i+1 and i-1
• Using tridiagonal Thomas algorithm allows to save computational time thanks to n complexity
• ? Python library with Thomas algorithm
• Numerical recipes, The Art of Scientific Computing 3rd Edition, William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery, 2007, isbn: 9780521880688
Ce site web utilise des cookies pour analyser le trafic de visites. En restant sur ce site, vous acceptez le stockage de cookies sur votre ordinateur. En savoir plus
• teaching/methcalchim/system_of_linear_equations.1539007604.txt.gz
• Dernière modification: 2018/10/08 16:06
• de villersd