Using the Tensor-Train Approach to Solve the Ground-State Eigenproblem for Hydrogen Molecules

DOI10.1137/15M102808XzbMath1360.65284OpenAlexW2592678397MaRDI QIDQ2968584

L. Ridgway Scott, Alexander Veit

Publication date: 20 March 2017

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m102808x

zbMATH Keywords

Born-Oppenheimer approximationlow-rank tensor approximationtensor-train formatschrödinger equation

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Multilinear algebra, tensor calculus (15A69)

Cites Work

• Tensor-Train Decomposition
• TT-cross approximation for multidimensional arrays
• Fast and accurate 3D tensor calculation of the Fock operator in a general basis
• The density-matrix renormalization group in the age of matrix product states
• \(O(d \log N)\)-quantics approximation of \(N\)-\(d\) tensors in high-dimensional numerical modeling
• Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators I. Separable approximation of multi-variate functions
• Tensor decomposition in electronic structure calculations on 3D Cartesian grids
• Incomplete cross approximation in the mosaic-skeleton method
• Approximation of boundary element matrices
• Black box approximation of tensors in hierarchical Tucker format
• Low-rank quadrature-based tensor approximation of the Galerkin projected Newton/Yukawa kernels
• A new scheme for the tensor representation
• A literature survey of low-rank tensor approximation techniques
• The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format
• Approximation of $2^d\times2^d$ Matrices Using Tensor Decomposition
• Tensor Spaces and Numerical Tensor Calculus
• Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions
• On the efficient computation of high-dimensional integrals and the approximation by exponential sums
• Van der Waals Interactions Between Two Hydrogen Atoms: The Slater--Kirkwood Method Revisited
• Numerical tensor calculus
• Low-Rank Explicit QTT Representation of the Laplace Operator and Its Inverse
• Solution of Linear Systems and Matrix Inversion in the TT-Format
• TT-GMRES: solution to a linear system in the structured tensor format
• Structured Rank-(r1, . . . , rd) Decomposition of Function-related Tensors in R_D
• Mathematical concepts of quantum mechanics.
• On tensor approximation of Green iterations for Kohn-Sham equations

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