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Shape Partition of Tensors and Eigenvalue Problem


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We co-authored a paper on novel applications of the nonlinear Perron–Frobenius theory which was published in the SIGEST section of SIAM Review.



QuantPi’s Chief Scientist and Co-Founder, Dr. Antoine Gautier, co-authored a paper on nonlinear spectral problems together with Francesco Tudisco from Gran Sasso Science Institute and Matthias Hein from Tübingen University.


The authors present a unifying Perron--Frobenius theory for nonlinear spectral problems defined in terms of nonnegative tensors. By using the concept of tensor shape partition, their results include, as a special case, a wide variety of particular tensor spectral problems considered in the literature and can be applied to a broad set of problems involving tensors (and matrices), including the computation of operator norms, graph and hypergraph matching in computer vision, hypergraph spectral theory, higher-order network analysis, and multimarginal optimal transport.


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