Adaptive methods for high-dimensional eigenvalue problems and their computational complexity (C09#)

高维特征值问题的自适应方法及其计算复杂度（C09

• 批准号: 396615020
• 金额: --
• 依托单位: Institut für Geometrie und Praktische Mathematik (IGPM)
• 依托单位国家: 德国
• 项目类别: Collaborative Research Centres
• 财政年份: 2018
• 资助国家: 德国
• 起止时间: 2017-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/396615020?language=en
• 关键词: Adaptive; methods; dimensional; eigenvalue; problems

The subject of this project are numerical solvers for high-dimensional eigenvalue problems that combine adaptive discretisations with low-rank representations of coefficient sequences. A main objective is to establish optimality properties concerning discretisation cardinalities, arising tensor ranks, and total computational complexity. This requires in particular new techniques for a posteriori error estimation and for preconditioning with low-rank tensor decompositions. As a particular application, Schrödinger equations in occupation number representation are considered.

该项目的主题是高维特征值问题的数值求解器，它将自适应离散化与系数序列的低秩表示相结合。主要目标是建立有关离散基数、上升张量秩和总计算复杂度的最优性属性。这特别需要用于后验误差估计和低秩张量分解预处理的新技术。作为一个特定的应用，考虑了占领数表示中的薛定谔方程。