Adaptive Simpler GMRES Based on Tensor Format for Sylvester Tensor Equation

The problem of Sylvester tensor equations is a crucial issue in several research applications. Krylov subspace methods are very e ective approaches to solve this problems due to their merits in large and sparse problems. We present an adaptive simpler GMRES method for solving the Sylvester tensor equation and then obtain an upper bound for condition num- ber of the basis matrix. Eventually, a numerical example is conducted to illustrate the e ectiveness of the method.