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Les deux révisions précédentes Révision précédente Prochaine révision | Révision précédente Prochaine révisionLes deux révisions suivantes | ||
teaching:methcalchim:system_of_linear_equations [2017/09/28 10:34] – villersd | teaching:methcalchim:system_of_linear_equations [2018/10/08 16:06] – villersd | ||
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Ligne 8: | Ligne 8: | ||
* [[wp> | * [[wp> | ||
* [[wp> | * [[wp> | ||
+ | * Chapter 2 in the book " | ||
+ | * 2.0 Introduction | ||
+ | * 2.1 Gauss-Jordan Elimination | ||
+ | * 2.2 Gaussian Elimination with Backsubstitution | ||
+ | * 2.3 LU Decomposition and Its Application | ||
+ | * Python [[https:// | ||
+ | * [[https:// | ||
* Time complexity analysis | * Time complexity analysis | ||
* Hint : in Python, use the timeit module | * Hint : in Python, use the timeit module | ||
- | ===== Applications | + | ===== Exercices and applications |
+ | * 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 | ||
==== 1D problems with neigbours ==== | ==== 1D problems with neigbours ==== | ||
* 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 | * 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 Thomas algorithm allows to save computational time thanks to n complexity | + | * Using [[wp> |
+ | * ? Python library with Thomas algorithm | ||
===== References : ===== | ===== References : ===== | ||
* Numerical recipes, The Art of Scientific Computing 3rd Edition, William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery, 2007, isbn: 9780521880688 | * Numerical recipes, The Art of Scientific Computing 3rd Edition, William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery, 2007, isbn: 9780521880688 | ||
* [[http:// | * [[http:// | ||
+ | * in C : [[http:// | ||
* [[http:// | * [[http:// | ||
* [[http:// | * [[http:// |