TY - JOUR ID - 4759 TI - A fast and efficient Newton-Shultz-type iterative method for computing inverse and Moore-Penrose inverse of tensors JO - Journal of Mathematical Modeling JA - JMM LA - en SN - 2345-394X AU - Khosravi Dehdezi, Eisa AU - Karimi, Saeed AD - Department of Mathematics, Persian Gulf University, Bushehr, Iran Y1 - 2021 PY - 2021 VL - 9 IS - 4 SP - 645 EP - 664 KW - Tensor KW - iterative methods KW - Moore-Penrose inverse KW - outer inverse KW - Einstein product DO - 10.22124/jmm.2021.19005.1627 N2 - A fast and efficient Newton-Shultz-type iterative method  is presented to compute the inverse of an invertible tensor. Analysis of the convergence error shows that the proposed method has the sixth order convergence. It is shown that the proposed algorithm can be used for finding the Moore-Penrose inverse of tensors. Computational complexities of the algorithm is presented to support the theoretical aspects of the paper. Using the  new method, we obtain a new preconditioner to solve the multilinear  system $\mathcal{A}\ast_N\mathcal{X}=\mathcal{B}$. The effectiveness and accuracy  of this method are re-verified by several numerical examples. Finally, some conclusions are given. UR - https://jmm.guilan.ac.ir/article_4759.html L1 - https://jmm.guilan.ac.ir/article_4759_0b3014f3bc2edf1193959cb9c4437a11.pdf ER -