teaching:methcalchim:system_of_linear_equations

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 teaching:methcalchim:system_of_linear_equations [2018/10/08 16:06]villersd teaching:methcalchim:system_of_linear_equations [2018/10/18 10:10]villersd 2018/10/18 10:10 villersd 2018/10/09 09:20 villersd 2018/10/08 16:06 villersd 2018/10/08 13:27 villersd 2017/09/28 10:39 villersd 2017/09/28 10:34 villersd 2016/11/25 11:15 villersd créée 2018/10/18 10:10 villersd 2018/10/09 09:20 villersd 2018/10/08 16:06 villersd 2018/10/08 13:27 villersd 2017/09/28 10:39 villersd 2017/09/28 10:34 villersd 2016/11/25 11:15 villersd créée Ligne 17: Ligne 17: * Time complexity analysis * Time complexity analysis * Hint : in Python, use the timeit module * Hint : in Python, use the timeit module + + ===== Jupyter notebooks ===== + * Example file (to be continued) : [[https://notebooks.azure.com/linusable/libraries/samples-public/html/notebooks/calculation_methods_applied_to_chemistry/Gauss-Jordan-01.ipynb]] ===== Exercices and applications ===== ===== Exercices and applications ===== Ligne 29: Ligne 32: * Using [[wp>Tridiagonal_matrix_algorithm|tridiagonal Thomas algorithm]] allows to save computational time thanks to n complexity * Using [[wp>Tridiagonal_matrix_algorithm|tridiagonal Thomas algorithm]] allows to save computational time thanks to n complexity * ? Python library with Thomas algorithm * ? Python library with Thomas algorithm + + ===== What you must have learned in this chapter ===== + * Except ill-conditionned, linear systems can be solved "exactly" using linear algebra algorithms in a finite and known number of arithmetic operations. + * The accuracy is determined by the number of numerical figures which are encoded in floating point description + * For a general system of n equations, diagonalisation requires of the order of n3 operations. Also for solving a system using these method. + * If the coefficient matrix is the same for different systems (only the independent coefficients are different), it is possible to solve systems with the order of n2 operations, if the matrix of coeeficients is decomposed in the product of two triangular matrix (Lower-Upper decomposition). This n3 step is realised only once. ===== References : ===== ===== References : =====
• teaching/methcalchim/system_of_linear_equations.txt
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