On the extensions of the GD inverse of tensors via the M-Product

Autor:	Jin, Hongwei, Chen, Siran, Huang, Shaowu, Stanimirović, Predrag S.
Rok vydání:	2024
Předmět:	Mathematics - Numerical Analysis Mathematical Physics
Druh dokumentu:	Working Paper
Popis:	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. Comment: 23 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.05799 Zobrazit plný text záznamu View this record from Arxiv