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arXiv · 2608.17157

Robust High-Order Projector-Splitting Integrators

Shiheng Zhang·Jingwei Hu
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Abstract

We develop a general framework for constructing robust high-order projector-splitting integrators for dynamical low-rank approximation. For a prescribed matrix increment, we show that the standard K-S-L projector-splitting step is equivalent to a reduced K-L step, thereby eliminating the explicit backward S-step. We then establish a central relaxed exactness property of the standard projector-splitting integrator: the rank-$r$ approximation inherits the accuracy of the numerical matrix increment, with an error bound independent of small singular values. The resulting schemes evolve fixed rank-$r$ factors and require neither basis augmentation nor rank truncation. As concrete examples, we combine the framework with selected second- and third-order Runge--Kutta methods to obtain robust high-order projector-splitting integrators. Numerical experiments confirm the predicted uniform convergence rates with respect to small singular values.

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Shiheng Zhang, Jingwei Hu. 2026-08-17. Robust High-Order Projector-Splitting Integrators. https://arxiv.org/abs/2608.17157

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