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 -