• Publications
  • Influence
The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format
TLDR
We present the first stable generic algorithm for the treatment of optimization tasks in the tensor format by a generalization of alternating least squares (ALS) algorithm and a modified approach (MALS) that enables dynamical rank adaptation. Expand
  • 219
  • 41
On manifolds of tensors of fixed TT-rank
TLDR
In this paper, we prove some new results for the TT representation of a tensor $${U \in \mathbb{R}^{n_1\times \cdots\times n_d}}$$ and for the manifold of tensors of TT-rank $${\underline{r}}$$ . Expand
  • 174
  • 15
  • PDF
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
  • 32
  • 6
  • PDF
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
  • 116
  • 5
  • PDF
On Local Convergence of Alternating Schemes for Optimization of Convex Problems in the Tensor Train Format
TLDR
We propose an according local linear convergence theory for the optimization of convex functionals $J$. Expand
  • 81
  • 5
  • PDF
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
  • 57
  • 3
  • PDF
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
  • 56
  • 2
  • PDF
Dynamical Approximation by Hierarchical Tucker and Tensor-Train Tensors
TLDR
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. 2360--2375]) to the recently proposed hierarchical Tucker (HT) tensor format (Hackbusch and Kuhn) and the tensor train (TT) format (Oseledets). Expand
  • 123
  • 1
  • PDF
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
  • 59
  • 1
  • PDF
Perturbed preconditioned inverse iteration for operator eigenvalue problems with applications to adaptive wavelet discretization
TLDR
We show that convergence is retained up to any tolerance if one only uses approximate applications of operators which leads to the perturbed preconditioned inverse iteration (PPINVIT) for elliptic operator eigenvalue problem. Expand
  • 18
  • 1
  • PDF