Koopman Spectral Linearization vs. Carleman Linearization: A Computational Comparison Study

Dongwei Shi and Xiu Yang ()
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Dongwei Shi: Department of Industrial and System Engineering, Lehigh University, Bethlehem, PA 18015, USA
Xiu Yang: Department of Industrial and System Engineering, Lehigh University, Bethlehem, PA 18015, USA

Mathematics, 2024, vol. 12, issue 14, 1-16

Abstract: Nonlinearity presents a significant challenge in developing quantum algorithms involving differential equations, prompting the exploration of various linearization techniques, including the well-known Carleman Linearization. Instead, this paper introduces the Koopman Spectral Linearization method tailored for nonlinear autonomous ordinary differential equations. This innovative linearization approach harnesses the interpolation methods and the Koopman Operator Theory to yield a lifted linear system. It promises to serve as an alternative approach that can be employed in scenarios where Carleman Linearization is traditionally applied. Numerical experiments demonstrate the effectiveness of this linearization approach for several commonly used nonlinear ordinary differential equations.

Keywords: quantum algorithms; differential equations; koopman operator; carleman linearization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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