A low-rank approach to the computation of path integrals
From MaRDI portal
Publication:2374948
DOI10.1016/j.jcp.2015.11.009zbMath1349.65549arXiv1504.06149OpenAlexW2162213884MaRDI QIDQ2374948
Mikhail S. Litsarev, Ivan V. Oseledets
Publication date: 5 December 2016
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1504.06149
convolutionpath integralFeynman-Kac formulalow-rank approximationmultidimensional integrationskeleton approximation
Brownian motion (60J65) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Tensor Decompositions and Applications
- Tensor-Train Decomposition
- TT-cross approximation for multidimensional arrays
- QTT-rank-one vectors with QTT-rank-one and full-rank Fourier images
- Fast evaluation of singular BEM integrals based on tensor approximations
- The DEPOSIT computer code based on the low rank approximations
- Convergence of difference scheme for heat equation in unbounded domains using artificial boundary conditions
- Sparse grid quadrature in high dimensions with applications in finance and insurance
- Adaptive cross approximation of multivariate functions
- \(O(d \log N)\)-quantics approximation of \(N\)-\(d\) tensors in high-dimensional numerical modeling
- Recompression techniques for adaptive cross approximation
- Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators I. Separable approximation of multi-variate functions
- Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators II. HKT representation of certain operators
- Tensor decomposition in electronic structure calculations on 3D Cartesian grids
- Tensor-structured preconditioners and approximate inverse of elliptic operators in \(\mathbb R^{d}\)
- Fast orthogonalization to the kernel of the discrete gradient operator with application to Stokes problem
- Fast and accurate tensor approximation of a multivariate convolution with linear scaling in dimension
- Mosaic-skeleton approximations
- Fast Fourier transform and convolution algorithms
- Extrapolation methods theory and practice
- Pseudo-skeleton approximations by matrices of maximal volume
- Numerical integration using sparse grids
- A theory of pseudoskeleton approximations
- Pseudoskeleton approximations of matrices
- Dimension-adaptive tensor-product quadrature
- Incomplete cross approximation in the mosaic-skeleton method
- Approximation of boundary element matrices
- Superfast Fourier transform using QTT approximation
- Hierarchical tensor-product approximation to the inverse and related operators for high-dimensional elliptic problems
- Artificial boundary conditions for diffusion equations: Numerical study
- Constructive representation of functions in low-rank tensor formats
- Approximation by exponential sums revisited
- A new scheme for the tensor representation
- Quantics-TT collocation approximation of parameter-dependent and stochastic elliptic PDEs
- Quantized-TT-Cayley transform for computing the dynamics and the spectrum of high-dimensional Hamiltonians
- An introduction to hierarchical (\(\mathcal H\)-) rank and TT-rank of tensors with examples
- Low rank Tucker-type tensor approximation to classical potentials
- Tensor-product approximation to operators and functions in high dimensions
- Multilevel Toeplitz Matrices Generated by Tensor-Structured Vectors and Convolution with Logarithmic Complexity
- A literature survey of low-rank tensor approximation techniques
- Sublinear Randomized Algorithms for Skeleton Decompositions
- Hierarchical Singular Value Decomposition of Tensors
- Approximation of $2^d\times2^d$ Matrices Using Tensor Decomposition
- QTT approximation of elliptic solution operators in higher dimensions
- Numerical Solution of the Hartree–Fock Equation in Multilevel Tensor-Structured Format
- Tensor conjugate-gradient-type method for Rayleigh quotient minimization in block QTT-format
- Tensor Spaces and Numerical Tensor Calculus
- Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions
- Accelerating Galerkin BEM for linear elasticity using adaptive cross approximation
- Path Integral Quantization and Stochastic Quantization
- Direct minimization for calculating invariant subspaces in density functional computations of the electronic structure
- Multigrid Accelerated Tensor Approximation of Function Related Multidimensional Arrays
- Diffusions and Elliptic Operators
- A Multilinear Singular Value Decomposition
- Numerical operator calculus in higher dimensions
- Numerical path integral techniques for long time dynamics of quantum dissipative systems
- Low-Rank Explicit QTT Representation of the Laplace Operator and Its Inverse
- Fast Solution of Parabolic Problems in the Tensor Train/Quantized Tensor Train Format with Initial Application to the Fokker--Planck Equation
- Fast Multidimensional Convolution in Low-Rank Tensor Formats via Cross Approximation
- Tensor-Structured Factorized Calculation of Two-Electron Integrals in a General Basis
- Tucker Dimensionality Reduction of Three-Dimensional Arrays in Linear Time
- Space-Time Approach to Non-Relativistic Quantum Mechanics
- Review of Feynman’s Path Integral in Quantum Statistics: from the Molecular Schrödinger Equation to Kleinert’s Variational Perturbation Theory
- BestN-term approximation in electronic structure calculations. II. Jastrow factors
- Geometric Numerical Integration
- Hamiltonian Path-Integral Methods
- Algorithms for Numerical Analysis in High Dimensions
- Approximation of 1/x by exponential sums in [1, ∞)
- Fast low‐rank approximations of multidimensional integrals in ion‐atomic collisions modelling
This page was built for publication: A low-rank approach to the computation of path integrals