RT info:eu-repo/semantics/article
T1 Computing tensor generalized inverses via specialization and rationalization
A1 Stanimirovic, Predrag S.
A1 Sendra Pons, Juan Rafael
A1 Behera, Ratikanta
A1 Sahoo, Jajati Keshari
A1 Mosic, Dijana
A1 Sendra Pons, Juana
A1 Lastra Sedano, Alberto
K1 Tensor
K1 Einstein product
K1 Tensors of functions
K1 Outer inverse
K1 Meromorphic functions
K1 Symbolic computation
K1 MatemÃ¡ticas
K1 Mathematics
AB In this paper, we introduce the notion of outer generalized inverses, with predefined range and none space, of tensors with rational function entries equipped with the Einstein product over an arbitrary field, of characteristic zero, with or without involution. We assume that the involved tensor entries are rational functions of unassigned variables or rational expressions of functional entries. The research investigates the replacements in two stages. The lower-stage replacements assume replacements of unknown variables by constant values from the field. The higher-order stage assumes replacements of functional entries by unknown variables. This approach enables the calculation on tensors over meromorphic functions to be simplified by analogous calculations on matrices whose elements are rational expressions of variables. In general, the derived algorithms permit symbolic computation of various generalized inverses which belong to the class of outer generalized inverses, with prescribed range and none space, over an arbitrary field of characteristic zero. More precisely, we focus on a few algorithms for symbolic computation of outer inverses of matrices whose entries are elements of a field of characteristic zero or a field of meromorphic functions in one complex variable over a connected open subset of C. Illustrative numerical results validate the theoretical results.
PB Springer Nature
SN 1578-7303
YR 2021
FD 2021-05-11
LK http://hdl.handle.net/10017/50517
UL http://hdl.handle.net/10017/50517
LA eng
NO Agencia Estatal de InvestigaciÃ³n
DS MINDS@UW
RD 04-jun-2023