Subspace Methods with Local Refinements for Eigenvalue Computation Using Low-Rank Tensor-Train Format

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• 作者：Junyu Zhang ; Zaiwen Wen ; Yin Zhang
• 关键词：High ; dimensional eigenvalue problem ; Tensor ; train format ; Alternating least square method ; Subspace optimization method
• 刊名：Journal of Scientific Computing
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：70
• 期：2
• 页码：478-499
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algorithms; Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theoretical, Mathematical and Computational Physics;
• 出版者：Springer US
• ISSN：1573-7691
• 卷排序：70

文摘

Computing a few eigenpairs from large-scale symmetric eigenvalue problems is far beyond the tractability of classic eigensolvers when the storage of the eigenvectors in the classical way is impossible. We consider a tractable case in which both the coefficient matrix and its eigenvectors can be represented in the low-rank tensor train formats. We propose a subspace optimization method combined with some suitable truncation steps to the given low-rank Tensor Train formats. Its performance can be further improved if the alternating minimization method is used to refine the intermediate solutions locally. Preliminary numerical experiments show that our algorithm is competitive to the state-of-the-art methods on problems arising from the discretization of the stationary Schrödinger equation.