Evaluating matrix power series with the Cayley-Hamilton theorem

2024/04/11 by Tobias Rindlisbacher, Rindlisbacher, Tobias
Physics and Astronomy · Mathematics · #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2404.07704

Abstract

The Cayley-Hamilton theorem is used to implement an iterative process for the efficient numerical computation of matrix power series and their differentials. In addition to straight-forward applications in lattice gauge theory simulations e.g. to reduce the computational cost of smearing, the method can also be used to simplify the evaluation of SU(N) one-link integrals or the computation of SU(N) matrix logarithms.

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