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methcalchimplugin-autotooltip__default plugin-autotooltip_bigCalculation methods applied to chemistry

Synopsis (english)

Mathematical prerequisites

Programming bases and tools

* Python programming language * LearnPython.org interactive tutorial with code execution * DataCamp free course "Intro to Python for Data Science" * Python 3 Tutorial, interactive, with code use in web browser * MOOCs (massive open online courses) :
1 Occurrences trouvées, Dernière modification:
.springer.com/statistics/computational+statistics/book/978-3-642-28069-6|Solving Differential Equations
root-finding_algorithmplugin-autotooltip__default plugin-autotooltip_bigRoot findings : equations f(x) = 0

* Polynomial equations : Bairstow's method is an efficient algorithm for finding the roots of a real polynomial of arbitrary degree * Polynomials in NumPy * polynomial module, including polyroots(c) to compute the roots of a polynomial.

* Bisection method (dichotomy) : very simple and robust method, but relatively slow. It assumes continuity of the function, and obtain one roots. The algorithm is based on a
1 Occurrences trouvées, Dernière modification:
thod|Newton-Raphson method]] * Chapter 9 in the book "Numerical Recipes" : Root finding an nonlinear s
system_of_linear_equationsplugin-autotooltip__default plugin-autotooltip_bigSystem 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
1 Occurrences trouvées, Dernière modification:
ward_and_back_substitution]] * Chapter 2 in the book "Numerical Recipes" : * 2.0 Introduction
numerical_integrationplugin-autotooltip__default plugin-autotooltip_bigNumerical integration

Error estimation

* Equally spaced methods : * Numerical_integration * Trapezoidal_rule * Newton–Cotes_formulas * Simpson's rule and composite Simpson's rule

* If intervals between interpolation points vary : * Gaussian_quadrature

* Chapter 4 in the book “Numerical Recipes” : Integration of Functions * 4.0 Introduction * 4.1 Classical Formulas for Equally Spaced Abscissas
1 Occurrences trouvées, Dernière modification:
* [[wp>Gaussian_quadrature]] * Chapter 4 in the book “Numerical Recipes” : Integration of Functions
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