142 citations · 712 across the 76 of their papers we have counts for
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Recovering orthogonal tensors under arbitrarily strong, but locally correlated, noise
Oscar Mickelin, Sertac Karaman
We consider the problem of recovering an orthogonally decomposable tensor with a subset of elements distorted by noise with arbitrarily large magnitude. We focus on the particular…
Multi-resolution Low-rank Tensor Formats
Oscar Mickelin, Sertac Karaman
We describe a simple, black-box compression format for tensors with a multiscale structure. By representing the tensor as a sum of compressed tensors defined on increasingly coarse…
Optimal orthogonal approximations to symmetric tensors cannot always be chosen symmetric
Oscar Mickelin, Sertac Karaman
We study the problem of finding orthogonal low-rank approximations of symmetric tensors. In the case of matrices, the approximation is a truncated singular value decomposition whic…
On Algorithms for and Computing with the Tensor Ring Decomposition
Oscar Mickelin, Sertac Karaman
Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional d…
A continuous analogue of the tensor-train decomposition
Alex A. Gorodetsky, Sertac Karaman, Youssef M. Marzouk
We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extensio…