The present work provides a comprehensive study of symmetric-conjugate operator splitting methods in the context of linear parabolic problems and demonstrates their additional benefits compared to symmetric splitting methods. Relevant applications include nonreversible systems and ground state computations for linear Schr\"odinger equations based on the imaginary time propagation. Numerical examples confirm the favourable error behaviour of higher-order symmetric-conjugate splitting methods and illustrate the usefulness of a time stepsize control, where the local error estimation relies on the computation of the imaginary parts and thus requires negligible costs.

翻译：本文系统研究了对称共轭算子分裂方法在线性抛物问题中的应用，并论证了其相较于对称分裂方法的额外优势。相关应用涵盖不可逆系统以及基于虚时传播的线性薛定谔方程基态计算。数值实验证实了高阶对称共轭分裂方法具有优越的误差特性，同时展示了时间步长控制的有效性——该方法通过计算虚部实现局部误差估计，从而显著降低计算成本。