Différences
Ci-dessous, les différences entre deux révisions de la page.
| Les deux révisions précédentes Révision précédente Prochaine révision | Révision précédente Prochaine révisionLes deux révisions suivantes | ||
| teaching:methcalchim:start [2020/09/01 09:52] – [Miscellaneous] villersd | teaching:methcalchim:start [2021/02/23 09:42] – [References] villersd | ||
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| Ligne 45: | Ligne 45: | ||
| * Diagonalisation and triangularisation | * Diagonalisation and triangularisation | ||
| * LU decomposition : factorization in triangular matrices | * LU decomposition : factorization in triangular matrices | ||
| - | * [[numerical_integration|Numerical intégration]] (integrals) | ||
| - | * Simpson method and gaussian quadratures | ||
| * [[root-finding_algorithm|Root findings : equations f(x) = 0]] | * [[root-finding_algorithm|Root findings : equations f(x) = 0]] | ||
| * Polynomial equations | * Polynomial equations | ||
| Ligne 52: | Ligne 50: | ||
| * Secant method, Regula falsi | * Secant method, Regula falsi | ||
| * Newton-Raphson method | * Newton-Raphson method | ||
| + | * [[numerical_integration|Numerical intégration]] (integrals) | ||
| + | * Simpson method and gaussian quadratures | ||
| + | |||
| + | <note tip> | ||
| + | Learning outcomes : | ||
| + | * Systems of linear equations | ||
| + | * failing of the theoretical way to solve a linear system using determinant and cofactors (np complexity) | ||
| + | * triangularisation and diagonalisation principles : algorithm and complexity | ||
| + | * " | ||
| + | * extension towards the matrix inversion | ||
| + | * lower-upper LU decomposition and complexity (N³ for the decomposition step and N² for substitution step). How to solve systems with varying independant vectors | ||
| + | * special matrix require special algorithms : tridiagonal matrix algorithm (Thomas algorithm) | ||
| + | * Root findings | ||
| + | * Bisection method (dichotomy) : simple and robust algorithm, invariant loop, slow convergence | ||
| + | * iterative transformation x = f(x), convergence and divergence situations | ||
| + | * secant and regula falsi methods, Convergence Criterion of the Fixed Point Method | ||
| + | * Newton-Raphson method (use of derivatives), | ||
| + | * Van Wijngaardeb-Dekker-Brent method (" | ||
| + | * Roots of polynomials and Bairstow' | ||
| + | * Numerical intégration | ||
| + | * Equally Spaced methods (trapezoidal, | ||
| + | * Gaussian Quadratures and orthogonal polynomials (special integrals, scale transformations, | ||
| + | </ | ||
| ==== Classical numerical methods ==== | ==== Classical numerical methods ==== | ||
| Ligne 151: | Ligne 172: | ||
| * chemistry | * chemistry | ||
| * misc docs : | * misc docs : | ||
| - | * [[https:// | + | * [[https:// |
| - | structures and reactions from the literature]] | + | * Blog articles |
| + | * [[https:// | ||