Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later

By C. Moler, Charles F. Van Loan. 1978

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Citations in the corpus

Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data (2020, background): “…the 3 D rotation group SO( 3 ), the translation and rotation group SE( d ) for d = 2 , 3 , the rotation-scale group R ∗ × SO( 2 ), and many others (Eade, 2014). an In the event that analytic solution is not available there are reliable numerical methods at our disposal (Moler and Van Loan, 2003).”
Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory (2005, unknown): “Computational methods are discussed in [426].”
Reachability Analysis and its Application to the Safety Assessment of Autonomous Cars (2010, methodology): “There exist many different techniques for the computation of the matrix exponential e [122].”
Low-rank tensor methods for linear systems and eigenvalue problems (2012, methodology): “In applications with large and possibly nonsymmetric A (i) L , different methods need to be used for approximating the matrix exponentials, see [56] for an overview.”
Continuous-time Monte Carlo methods for quantum impurity models (2010, background): “Computing the exponential of a matrix (Moler and Loan, 2003) is an expensive operation.”
DECAY BOUNDS AND ( ) ALGORITHMS FOR APPROXIMATING FUNCTIONS OF SPARSE MATRICES (2007, background): “... from the large body of existing work, we point out that much of the literature on the approximation of matrix functions falls into two broad classes: 1. Algorithms designed for the “exact” (i.e., high-accuracy) computation of f(A), where A is a dense matrix of moderate size; here f is often some”
The Magnus expansion and some of its applications (2008, background): “An important reference in this context is [177] and its updated version [178], where up to nineteen (or twenty in [178]) different numerical algorithms for computing the exponential of a matrix are carefully reviewed.”