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Nonlocal Matrix Rank Minimization Method for Multiplicative Noise Removal
Multiplicative noise removal is a challenging problem in image denoising. In this paper, we develop a nonlocal matrix rank minimization method for...
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Reconstructing Planar Ellipses from Translation-Invariant Minkowski Tensors of Rank Two
Minkowski tensors contain information about shape and orientation of the underlying convex body. We make this precise by showing that reconstructing...
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An Adaptive Dynamical Low Rank Method for the Nonlinear Boltzmann Equation
Efficient and accurate numerical approximation of the full Boltzmann equation has been a longstanding challenging problem in kinetic theory. This is...
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Adaptive Integration of Nonlinear Evolution Equations on Tensor Manifolds
We develop new adaptive algorithms for temporal integration of nonlinear evolution equations on tensor manifolds. These algorithms, which we call...
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A System of Sylvester-like Quaternion Tensor Equations with an Application
This paper establishes the solvability conditions and an expression of the exact solution to a system of three Sylvester-like quaternion tensor...
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Hot-SVD: higher order t-singular value decomposition for tensors based on tensor–tensor product
This paper considers a way of generalizing the t-SVD of third-order tensors (regarded as tubal matrices) to tensors of arbitrary order
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Provable Stochastic Algorithm for Large-Scale Fully-Connected Tensor Network Decomposition
The fully-connected tensor network (FCTN) decomposition is an emerging method for processing and analyzing higher-order tensors. For an N th-order...
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Approximate Bayesian Algorithm for Tensor Robust Principal Component Analysis
Srakar, AndrejRecently proposed Tensor Robust Principal Component Analysis (TRPCA) (Lu et al. in Tensor robust principal component analysis: exact...
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The partially symmetric rank-1 approximation of fourth-order partially symmetric tensors
Finding the partially symmetric rank-1 approximation to a given fourth-order partially symmetric tensor has close relationship with its largest M -eige...
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Tensor Product Operators
As everywhere in this book, all linear spaces are over the same field $${\mathbb...
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The Set of Orthogonal Tensor Trains
In this paper we study the set of tensors that admit a special type of decomposition called an orthogonal tensor train decomposition. Finding...
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The Fréchet derivative of the tensor t-function
The tensor t-function , a formalism that generalizes the well-known concept of matrix functions to third-order tensors, is introduced in Lund (Numer...
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Tensor Products
Tensor products is the study of multilinear maps by linear maps, meaning that the multilinear maps from a space factor uniquely through a linear map...
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Communication Lower Bounds for Nested Bilinear Algorithms via Rank Expansion of Kronecker Products
We develop lower bounds on communication in the memory hierarchy or between processors for nested bilinear algorithms, such as Strassen’s algorithm...
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Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions
We study the approximation of univariate functions by combining tensorization of functions with tensor trains (TTs)—a commonly used type of tensor...
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Non-negative low-rank approximations for multi-dimensional arrays on statistical manifold
Although low-rank approximation of multi-dimensional arrays has been widely discussed in linear algebra, its statistical properties remain unclear....
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Function Theory from Tensor Algebras
We survey connections between our work on tensor algebras over \(C^*\)...
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Generative modeling via tree tensor network states
In this paper, we present a density estimation framework based on tree tensor-network states. The proposed method consists of determining the tree...
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Tensor product and inverse fractional abstract Cauchy problem
In this paper, we find atomic solution and finite rank function solution for fractional abstract Cauchy problem. The fractional derivative used is...
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Perturbation Analysis for t-Product-Based Tensor Inverse, Moore-Penrose Inverse and Tensor System
This paper establishes some perturbation analysis for the tensor inverse, the tensor Moore-Penrose inverse, and the tensor system based on the...