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The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format
Recent achievements in the field of tensor product approximation provide promising new formats for the representation of tensors in form of tree tensor networks. In contrast to the canonical $r$-termExpand
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On manifolds of tensors of fixed TT-rank
Recently, the format of TT tensors (Hackbusch and Kühn in J Fourier Anal Appl 15:706–722, 2009; Oseledets in SIAM J Sci Comput 2009, submitted; Oseledets and Tyrtyshnikov in SIAM J Sci Comput 31:5,Expand
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DIRECT MINIMIZATION FOR CALCULATING INVARIANT SUBSPACES IN DENSITY FUNCTIONAL COMPUTATIONS OF THE ELECTRONIC STRUCTURE
在这篇文章,我们分析最陡峭的降下算法,象不变的 subspace 计算一样在 Hartree-Fock 和 Kohn 假冒的理论部分流行,由 orthogonality 条件抑制了的三相关 preconditioned。我们利用几何学可被考虑歧管,即,关于单一的转变的 invaxiance,到再用形式表示象可被考虑的集合歧管的 Grassmann 上的问题。我们然后在相应 LagrangianExpand
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An analysis for the DIIS acceleration method used in quantum chemistry calculations
This work features an analysis for the acceleration technique DIIS that is standardly used in most of the important quantum chemistry codes, e.g. in DFT and Hartree–Fock calculations and in theExpand
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On Local Convergence of Alternating Schemes for Optimization of Convex Problems in the Tensor Train Format
Alternating linear schemes (ALS), with the alternating least squares algorithm a notable special case, provide one of the simplest and most popular choices for the treatment of optimization tasks byExpand
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Error estimates for the Coupled Cluster method
The Coupled Cluster (CC) method is a widely used and highly successful high precision method for the solution of the stationary electronic Schrodinger equation , with its practical convergenceExpand
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The continuous Coupled Cluster formulation for the electronic Schrödinger equation
Nowadays, the Coupled Cluster (CC) method is the probably most widely used high precision method for the solution of the main equation of electronic structure calculation, the stationary electronicExpand
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Dynamical Approximation by Hierarchical Tucker and Tensor-Train Tensors
We extend results on the dynamical low-rank approximation for the treatment of time-dependent matrices and tensors (Koch and Lubich; see [SIAM J. Matrix Anal. Appl., 29 (2007), pp. 434--454], [SIAMExpand
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The Alternating Linear Scheme for Tensor Optimisation in the TT Format
Recent achievements in the field of tensor product approximation [11, 32] provide promising new formats for the representation of tensors in form of tree tensor networks. In contrast to the canonicalExpand
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Perturbed preconditioned inverse iteration for operator eigenvalue problems with applications to adaptive wavelet discretization
In this paper we discuss an abstract iteration scheme for the calculation of the smallest eigenvalue of an elliptic operator eigenvalue problem. A short and geometric proof based on theExpand
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