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Ci-dessous, les différences entre deux révisions de la page.

--- teaching:methcalchim:system_of_linear_equations [2016/11/25 11:15] – créée villersd
+++ teaching:methcalchim:system_of_linear_equations [2017/09/28 10:39] – villersd
@@ Ligne 2: / Ligne 2: @@
 <note tip>Numerical methods used to solve such problem allow to introduce and experiment on [[wp>Time_complexity]], considering cubic time behavior of standard algorithms and //i.e.// quadratic time solutions using LU decomposition.</note>
+===== Theory =====
   * [[wp>System_of_linear_equations]]
   * [[wp>Gaussian_elimination]], Gauss and Gauss-Jordan eliminations (diagonalization, triangularization)
@@ Ligne 10: / Ligne 11: @@
     * Hint : in Python, use the timeit module
-References :
+===== 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 ====
+  * 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 [[wp>Tridiagonal_matrix_algorithm|tridiagonal Thomas algorithm]] allows to save computational time thanks to n complexity
+  * ? Python libraty with Thomas algorithm
+===== 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
     * [[http://numerical.recipes/]]
     * [[http://www2.units.it/ipl/students_area/imm2/files/Numerical_Recipes.pdf]]
     * [[http://apps.nrbook.com/empanel/index.html#]]