Let Ω1 ⊂ R n1 and Ω2 ⊂ R n2 be two given domains and consider on each domain a multiscale sequence of ansatz spaces of polynomial exactness r1 and r2, respectively. In this paper, we study the optimal construction of sparse tensor products made from these spaces. In particular, we derive

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It has become routine to collect data that are structured as multiway arrays (tensors). There is an enormous literature on low rank and sparse matrix factorizations, but limited consideration of exten-sions to the tensor case in statistics. The most common low rank tensor factorization relies

The Canonical Polyadic Decomposition (CPD) of tensors is a powerful tool for analyzing multi-way data and is used ex-tensively to analyze very large and extremely sparse datasets. The bottleneck of computing the CPD is multiplying a sparse tensor by several dense matrices. Algorithms for tensor

In this paper, we present a novel compression technique for Bidirectional Texture Functions based on a sparse tensor decomposition. We apply the K-SVD algorithm along two different modes of a tensor to decompose it into a small dictionary and two sparse tensors. This representation is very compact

Multi-dimensional arrays, or tensors, are increasingly found in fields such as signal processing and recommender systems. Real-world tensors can be enormous in size and often very sparse. There is a need for efficient, high-performance tools capable of processing the massive sparse tensors

Block sparsity was employed recently in vector/matrix based sparse representations to improve their performance in signal classification. It is known that tensor based representation has potential advantages over vector/matrix based representation in retaining the spatial distributions within

Abstract. For Au = f with an elliptic differential operator A: H → H ′ and stochastic data f, the m-point correlation function Mmu of the random solution u satisfies a deterministic, hypoelliptic equation with the m-fold tensor product operatorA(m) of A. Sparse tensor products of hierarchic FE

Abstract. On product domains, sparse-grid approximation yields optimal, dimension independent convergence rates when the function that is approximated has L 2-bounded mixed derivatives of a sufficiently high order. We show that the solution of Poisson’s equation on the n-dimensional hypercube

Funding: in collaboration with ABB corporate research