Global and extended global Hessenbergprocesses for solving Sylvester tensorequation with low-rank right-hand side

In this paper, we introduce two new schemes based on the global hessenbergprocesses for computing approximate solutions to low-rank sylvestertensor equations. we first construct bases for the matrix and extendedmatrix krylov subspaces by applying the global and extended global hessenbergprocesses. then the initial problem is projected into the matrixor extended matrix krylov subspaces with small dimensions. the reducedsylvester tensor equation obtained by the projection methods can be solvedby using a recursive blocked algorithm. furthermore, we present the upperbounds for the residual tensors without requiring the computation of theapproximate solutions in any iteration. finally, we illustrate the performanceof the proposed methods with some numerical examples.