论文标题
用于动力学低级近似的非常规的鲁棒积分器
An unconventional robust integrator for dynamical low-rank approximation
论文作者
论文摘要
我们提出和分析了一个数值集成符，该数字积分器计算出低级别近似值的大型时间依赖性矩阵，该矩阵通过其增量明确给出，或者是矩阵微分方程的未知解决方案。此外，积分器被扩展到固定多线性等级的Tucker张量的时间相关张量的近似。所提出的低级积分器与用于动态低级别近似的已知投影仪分解积分器不同，但它保留了对小奇异值的重要鲁棒性，迄今为止，仅因投影仪切开的集成符而闻名。新的集成商还提供了与投影仪分拆集成器相比的一些潜在优势：它避免了投影仪拆分集成器的向后时间集成取代，这是耗散问题的潜在不稳定的取代。它提供了更多的并行性，并且在微分方程执行时，可以保留矩阵或张量的对称或反对称。数值实验说明了提出的集成器的行为。
We propose and analyse a numerical integrator that computes a low-rank approximation to large time-dependent matrices that are either given explicitly via their increments or are the unknown solution to a matrix differential equation. Furthermore, the integrator is extended to the approximation of time-dependent tensors by Tucker tensors of fixed multilinear rank. The proposed low-rank integrator is different from the known projector-splitting integrator for dynamical low-rank approximation, but it retains the important robustness to small singular values that has so far been known only for the projector-splitting integrator. The new integrator also offers some potential advantages over the projector-splitting integrator: It avoids the backward time integration substep of the projector-splitting integrator, which is a potentially unstable substep for dissipative problems. It offers more parallelism, and it preserves symmetry or anti-symmetry of the matrix or tensor when the differential equation does. Numerical experiments illustrate the behaviour of the proposed integrator.
