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 [2019/12/12 08:46] – [Miscellaneous] villersd | teaching:methcalchim:start [2021/01/22 13:31] – [Fundamental numerical methods] 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 100: | Ligne 121: | ||
=== Chebyshev approximation === | === Chebyshev approximation === | ||
+ discussion of some approximations like [[wp> | + discussion of some approximations like [[wp> | ||
+ | * [[https:// | ||
=== Molecules modelisation and visualization === | === Molecules modelisation and visualization === | ||
Ligne 176: | Ligne 198: | ||
* [[https:// | * [[https:// | ||
* [[https:// | * [[https:// | ||
+ | * [[https:// | ||
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