Spectral tensor-train decomposition (Q2818241)

scientific article; zbMATH DE number 6624656

Language	Label	Description	Also known as
English	Spectral tensor-train decomposition	scientific article; zbMATH DE number 6624656

Statements

instance of

scholarly article

0 references

author

Daniele Bigoni

0 references

Allan P. Engsig-Karup

0 references

Youssef M. Marzouk

0 references

published in

SIAM Journal on Scientific Computing

0 references

publication date

7 September 2016

0 references

full work available at URL

https://arxiv.org/abs/1405.5713

0 references

zbMATH Keywords

approximation theory

0 references

tensor-train decomposition

0 references

orthogonal polynomials

0 references

uncertainty quantification

0 references

describes a project that uses

0 references

0 references

0 references

0 references

0 references

0 references

High dimensional polynomial interpolation on sparse grids

0 references

Polynomial interpolation results in Sobolev spaces

0 references

Chebyshev and Fourier spectral methods.

0 references

The Mathematical Theory of Finite Element Methods

0 references

Spectral Methods

0 references

Analysis of individual differences in multidimensional scaling via an $n$-way generalization of ``Eckart-Young'' decomposition

0 references

The proper generalized decomposition for advanced numerical simulations. A primer

0 references

On selecting a maximum volume sub-matrix of a matrix and related problems

0 references

Adaptive Smolyak Pseudospectral Approximations

0 references

Sparse pseudospectral approximation method

0 references

Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem

0 references

Polynomial Chaos Expansion of Random Coefficients and the Solution of Stochastic Partial Differential Equations in the Tensor Train Format

0 references

A least-squares approximation of partial differential equations with high-dimensional random inputs

0 references

Non-intrusive low-rank separated approximation of high-dimensional stochastic models

0 references

Efficient low-rank approximation of the stochastic Galerkin matrix in tensor formats

0 references

Q4820343

0 references

To Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations---the “Plain Vanilla” Galerkin Case

0 references

Calculation of Gauss Quadrature Rules

0 references

Q3086656

0 references

Pseudo-skeleton approximations by matrices of maximal volume

0 references

Hierarchical Singular Value Decomposition of Tensors

0 references

A literature survey of low-rank tensor approximation techniques

0 references

Tensor Spaces and Numerical Tensor Calculus

0 references

A new scheme for the tensor representation

0 references

Q4171170

0 references

Q5756148

0 references

Q3965154

0 references

$O(d \log N)$-quantics approximation of $N$-$d$ tensors in high-dimensional numerical modeling

0 references

Quantics-TT collocation approximation of parameter-dependent and stochastic elliptic PDEs

0 references

Tensor-Structured Galerkin Approximation of Parametric and Stochastic Elliptic PDEs

0 references

Tensor Decompositions and Applications

0 references

Implementing Spectral Methods for Partial Differential Equations

0 references

Q4146094

0 references

Sampling and Low-Rank Tensor Approximation of the Response Surface

0 references

Q4165953

0 references

Solving stochastic systems with low-rank tensor compression

0 references

A Jacobi-Type Method for Computing Orthogonal Tensor Decompositions

0 references

An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data

0 references

Proper generalized decompositions and separated representations for the numerical solution of high dimensional stochastic problems

0 references

Generalized spectral decomposition for stochastic nonlinear problems

0 references

Approximation of $2^d\times2^d$ Matrices Using Tensor Decomposition

0 references

Tensor-Train Decomposition

0 references

Constructive representation of functions in low-rank tensor formats

0 references

TT-cross approximation for multidimensional arrays

0 references

The Optimum Addition of Points to Quadrature Formulae

0 references

Approximation rates for the hierarchical tensor format in periodic Sobolev spaces

0 references

Karhunen-Loève approximation of random fields by generalized fast multipole methods

0 references

The Eigen-Values and Singular Values of Integral Equations<sup>†</sup>

0 references

Q5600030

0 references

Model reduction based on proper generalized decomposition for the stochastic steady incompressible Navier-Stokes equations

0 references

Continuous analogues of matrix factorizations

0 references

Q4337625

0 references

Tensor approximations of matrices generated by asymptotically smooth functions

0 references

The best $L^ 2$-approximation by finite sums of functions with separable variables

0 references

High-Order Collocation Methods for Differential Equations with Random Inputs

0 references

title

Spectral tensor-train decomposition (English)

0 references

Identifiers

zbMATH Open document ID

1347.41006

0 references

DOI

10.1137/15M1036919

0 references

Mathematics Subject Classification ID

0 references

0 references

0 references

0 references

0 references

0 references

0 references

0 references

Sitelinks

Mathematics(1 entry)

mardi Publication:2818241