https://dvillers.umons.ac.be/wiki/ 2026-05-03T12:19:16+00:00 https://dvillers.umons.ac.be/wiki/ https://dvillers.umons.ac.be/wiki/_media/favicon.ico text/html 2021-06-11T12:15:10+00:00 Anonymous (anonymous@undisclosed.example.com) https://dvillers.umons.ac.be/wiki/teaching:methcalchim:eigenvalues_and_eigenvectors?rev=1623406510&do=diff Eigenvalues and eigenvectors * Eigenvalues and eigenvectors * Important matrix properties * Hermitian, orthogonality,... * Eigenvalue algorithm * Power iteration, a simple numerical algorithm producing a number $\lambda$, the greatest (in absolute value) eigenvalue of a matrix $A$, and the corresponding eigenvector $v$$Av=\lambda v$ text/html 2022-03-17T08:50:35+00:00 Anonymous (anonymous@undisclosed.example.com) https://dvillers.umons.ac.be/wiki/teaching:methcalchim:partial_differential_equation?rev=1647503435&do=diff Numerical solutions of PDE * Finite element method * Finite volume method * Boundary element method * Spectral method * Multigrid methods * ... * Numerical partial differential equations However, the finite difference method can be more easliy applied to a lot of classical PDE. In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.$$\frac{\partial T}{\partial t} = \kappa\left(\frac{… text/html 2018-10-18T10:10:41+00:00 Anonymous (anonymous@undisclosed.example.com) https://dvillers.umons.ac.be/wiki/teaching:methcalchim:system_of_linear_equations?rev=1539850241&do=diff System of linear equations Time_complexityi.e. Theory * System_of_linear_equations * Gaussian_elimination, Gauss and Gauss-Jordan eliminations (diagonalization, triangularization) * Pivot_element, pivoting * LU_decomposition * Triangular_matrix * Chapter 2 in the book “Numerical Recipes” : * 2.0 Introduction * 2.1 Gauss-Jordan Elimination