2024/12/08 by Jin, Hongwei, Chen, Siran, Huang, Shaowu +1
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2412.05799
We study extensions of the GD tensor inverse using the M-product. The aim of current research is threefold. In the first place, the tensor GD inverse under the M-product is introduced and considered. We give the several properties and representations of the GD inverse using the core nilpotent decomposition and then establish the reverse-order law rules for the GD inverse. Second, the tensor GDMP inverse is studied and the corresponding numerical algorithm is given. In addition, the reverse- and forward-order laws of the GDMP inverse are established. Third, the GD-Star tensor inverse under the M-product is introduced and studied. Finally, the GD inverse, GDMP inverse and GD-Star inverse solutions of multilinear equations are investigated. Illustrative numerical calculation is performed.