A New Scaling and Squaring Algorithm for the Matrix Exponential

By Awad H. Al-Mohy, Nicholas John Higham. SIAM Journal on Matrix Analysis and Applications, 2009

387 citations recorded by the source corpus.

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Moser Flow: Divergence-based Generative Modeling on Manifolds (2021, background): “On the hyperboloid, on the other hand, the exponential map is numerically not well-behaved far away from the origin (Dooley and Wildberger, 1993; Al-Mohy and Higham, 2010).”
DAGs with NO TEARS: Continuous Optimization for Structure Learning (2018, background): “A key conclusion from Theorem 1 is that h and its gradient only involve evaluating the matrix exponential, which is a well-studied function in numerical analysis, and whose O ( d 3 ) algorithm (Al-Mohy and Higham, 2009) is readily available in many scientiﬁc computing libraries.”
Cheap Orthogonal Constraints in Neural Networks: A Simple Parametrization of the Orthogonal and Unitary Group (2019, methodology): “We have that The differential of the exponential of matrices (d exp) A can be approximated to machine-precision computing the exponential of a 2 n × 2 n matrix, as described in (Al-Mohy & Higham, 2009a).”