Concept

Tensor product

Related publications (123)

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COMMUNICATION LOWER BOUNDS AND OPTIMAL ALGORITHMS FOR MULTIPLE TENSOR-TIMES-MATRIX COMPUTATION

Laura Grigori

Multiple tensor-times-matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower bounds that determine ...

Philadelphia2024

Low-Rank Tensor Methods for High-Dimensional Problems

Christoph Max Strössner

In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...

EPFL2023

Rank-Adaptive Time Integration Of Tree Tensor Networks

Gianluca Ceruti

A rank-adaptive integrator for the approximate solution of high-order tensor differential equations by tree tensor networks is proposed and analyzed. In a recursion from the leaves to the root, the integrator updates bases and then evolves connection tenso ...

SIAM PUBLICATIONS2023

High order geometric methods with splines: fast solution with explicit time-stepping for Maxwell equations

Bernard Kapidani, Rafael Vazquez Hernandez

We introduce a high-order spline geometric approach for the initial boundary value problem for Maxwell's equations. The method is geometric in the sense that it discretizes in structure preserving fashion the two de Rham sequences of differential forms inv ...

2023

The unipotent mixing conjecture

Philippe Michel

We show that shifted pairs of discrete or continuous low-lying horocycles equidistribute in the product space of two modular curves. ...

Jerusalem2023

Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...

WORLD SCIENTIFIC PUBL CO PTE LTD2023

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In this letter we consider mean field type control problems with multiple species that have different dynamics. We formulate the discretized problem using a new type of entropy-regularized multimarginal optimal transport problems where the cost is a decomp ...

2023

STREAMING TENSOR TRAIN APPROXIMATION

Daniel Kressner

Tensor trains are a versatile tool to compress and work with high-dimensional data and functions. In this work we introduce the streaming tensor train approximation (STTA), a new class of algorithms for approximating a given tensor ' in the tensor train fo ...

Philadelphia2023

We provide a new description of the complex computing the Hochschild homology of an -unitary -algebra as a derived tensor product such that: (1) there is a canonical morphism from it to the complex computing the cyclic homology of that was introduced by Ko ...

2023

The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of empirical means of de ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2023