The paper derives tensor versions of rational Arnoldi and Lanczos algorithms for model reduction and tensor Lyapunov equations, but they are equivalent to existing matrix methods after unfolding.
Barraud, A numerical algorithm to solve atxa- x = q, IEE E Transac
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A rational Krylov methods for large scale linear multidimensional dynamical systems
The paper derives tensor versions of rational Arnoldi and Lanczos algorithms for model reduction and tensor Lyapunov equations, but they are equivalent to existing matrix methods after unfolding.