84 citations · 244 across the 10 of their papers we have counts for
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The contractivity of cone-preserving multilinear mappings
Antoine Gautier, Francesco Tudisco
With the notion of mode- Birkhoff contraction ratio, we prove a multilinear version of the Birkhoff-Hopf and the Perron-Fronenius theorems, which provide conditions on the exist…
The Perron-Frobenius theorem for multi-homogeneous mappings
Antoine Gautier, Francesco Tudisco, Matthias Hein
The Perron-Frobenius theory for nonnegative matrices has been generalized to order-preserving homogeneous mappings on a cone and more recently to nonnegative multilinear forms. We…
A unifying Perron-Frobenius theorem for nonnegative tensors via multi-homogeneous maps
Antoine Gautier, Francesco Tudisco, Matthias Hein
We introduce the concept of shape partition of a tensor and formulate a general tensor eigenvalue problem that includes all previously studied eigenvalue problems as special cases.…
The Perron-Frobenius Theorem for Multi-homogeneous Maps
Antoine Gautier, Francesco Tudisco, Matthias Hein
We introduce the notion of order-preserving multi-homogeneous mapping which allows to study Perron-Frobenius type theorems and nonnegative tensors in unified fashion. We prove a we…
Tensor norm and maximal singular vectors of non-negative tensors - a Perron-Frobenius theorem, a Collatz-Wielandt characterization and a generalized power method
Antoine Gautier, Matthias Hein
We study the l^{p_1,...,p_m} singular value problem for non-negative tensors. We prove a general Perron-Frobenius theorem for weakly irreducible and irreducible nonnegative tensors…