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--- teaching:ft1920:praktikum:start [2019/09/20 12:37]
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+++ teaching:ft1920:praktikum:start [2021/03/02 13:28] (current)
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-====== Programmierpraktikum ======
+====== Exponential Integrators with PyTorch ======
-More Information coming soon.
+===== Organisation =====
+{{teaching:ft1920:praktikum:files:programmierpraktikum.pdf | Slides from the Introduction}}
+===== Literature =====
+==== Introduction ====
+    * {{teaching:ft1920:praktikum:files:niesen_and_wright_-_algorithm_919_a_krylov_subspace_algorithm_for_eva.pdf|Niesen, Wright - Algorithm 919: A Krylov Subspace Algorithm for Evaluating the φ-Functions Appearing in Exponential Integrators}} Good introduction, idea of time stepping
+==== Special topics ====
+    * {{teaching:ft1920:praktikum:files:al-mohy_higham_-_computing_the_action_of_the_matrix_exponential_with_an_application_to_exponential_integrators.pdf| Al-Hohy, Higham - Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators}} computing $e^A B$, computing $e^{tA} B$ over a time intervall
+    * {{hochbruck_and_lubich_-_1997_-_on_krylov_subspace_approximations_to_the_matrix_ex.pdf| Hochbruck, Lubich - On Krylov subspace approximations to the Matrix Exponential Operator}} Error bounds
+    * {{teaching:ft1920:praktikum:files:saad_-_analysis_of_some_krylov_subspace_approximations_to.pdf|Saad - Analysis of some Krylov Subspace Approximations to the Matrix Exponential Operator}} Error bounds
+==== Matrix Exponential ====
+    * {{teaching:ft1920:praktikum:files:moler2003_-_nineteen_dubious_ways_to_compute_the_exponential_of_a_matrix_twenty_five_years_later.pdf|Moler, Van Loan - Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later}} this paper is the definitive guide on how to calculate the exponential of a matrix
+==== Application of Exponential Integrators ====
+    * {{teaching:ft1920:praktikum:files:hochbruck_and_ostermann_-_exponential_integrators.pdf|Hochbruck, Ostermann - Exponential integrators}} application to stiff problems
+==== Software ====
+    * {{teaching:ft1920:praktikum:files:sidje_-_expokit_a_software_package_for_computing_matrix_exponentials.pdf| Sidje - Expokit: A Software Package for ComputingMatrix Exponentials}} Expokit is a Fortran/Matlab implementation of exponential integrators, the paper contains a lot of useful details on implementing exponential integrators.