An algorithm for calculating spectral radius of $s$-index weakly positive tensors

In this paper, we introduced $s$-index weakly positive tensors and discussed the calculation of the spectral radius of this kind of nonnegative tensors. Using the diagonal similarity transformation of tensor and Perron-Frobenius theory of nonnegative tensor, the calculation method of the maximum $H$-eigenvalue of $s$-index weakly positive tensors was given. A variable parameter was introduced in each iteration of the algorithm, which is equivalent to a translation transformation of the tensor in each iteration to improve the calculation speed. At the same time, it was proved that the algorithm is linearly convergent for the calculation of the spectral radius of $s$-index weakly positive tensors. The final numerical example shows the effectiveness of the algorithm.