| Abstract: | Tensors have a wide application in control systems, documents analysis,medical engineering, formulating an $n$-person noncooperative game and so on. It isthe purpose of this paper to explore two efficient and novel algorithms for computingthe solutions $mathcal{X}$ and $mathcal{Y}$ of the high order tensor equation $mathcal{A}*_Pmathcal{X}*_Qmathcal{B}+mathcal{C}*_Pmathcal{Y}*_Qmathcal{D}=mathcal{H}$ with Einstein product. The algorithms are, respectively, based on the Hestenes-Stiefel (HS) and the Lanczos types of bi-conjugate residual (Bi-CR) algorithm. The theoretical results indicate that the algorithms terminate after finitely many iterationswith any initial tensors. The resulting algorithms are easy to implement and simpleto use. Finally, we present two numerical examples that confirm our analysis andillustrate the efficiency of the algorithms. |
