Nonlinear Perron-Frobenius theorems for nonnegative tensors
SIAM Review (SIGEST paper), vol. 65, pp. 495–536, 2023
We present a unifying Perron–Frobenius theory for nonlinear spectral problems defined in terms of nonnegative tensors. By using the concept of tensor shape partition, our 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 …
A unifying Perron-Frobenius theorem for nonnegative tensors via multihomogeneous maps
SIAM Journal on Matrix Analysis and Applications, vol. 40, pp. 1206–1231, 2019
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. We formulate irreducibility and symmetry properties of a nonnegative tensor $T$ in terms of the associated shape partition. We recast the …
The Perron-Frobenius theorem for multihomogeneous mappings
SIAM Journal on Matrix Analysis and Applications, vol. 40, pp. 1179–1205, 2019
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 unify both approaches by introducing the concept of order-preserving multi-homogeneous mappings, their associated nonlinear spectral …