Exponential Integrators with PyTorch

Slides from the Introduction

• Niesen, Wright - Algorithm 919: A Krylov Subspace Algorithm for Evaluating the φ-Functions Appearing in Exponential Integrators Good introduction, idea of time stepping

• 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, Lubich - On Krylov subspace approximations to the Matrix Exponential Operator Error bounds
• Saad - Analysis of some Krylov Subspace Approximations to the Matrix Exponential Operator Error bounds

• 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

• Hochbruck, Ostermann - Exponential integrators application to stiff problems

• 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.