Perturbation analysis of tensor $(\mathcal{B},\mathcal{C})$-inverse via Einstein product
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910026588749824 |
|---|---|
| author | Zhang, Daochang Li, Jingqian Mosic, Dijana Stanimirovic, Predrag S. |
| author_facet | Zhang, Daochang Li, Jingqian Mosic, Dijana Stanimirovic, Predrag S. |
| contents | We investigate the influence of a relatively small perturbation on various generalized inverses functions or quantities derived from a tensor $\mathcal{A}$.When a small tensor perturbation \(\mathcal{E}\) is introduced, it becomes challenging to analyze generalized inverses of the perturbed tensor \( \mathcal{D} =\mathcal{A}+\mathcal{E}\) and to determine how this perturbation affects a generalized inverse of $\mathcal{A}$.Our main goal is to understand the relationship between $\mathcal{D}^\Game$ and \( \mathcal{A}^\Game \), where $(\cdot)^\Game$ denotes a specific generalized inverse or a class of generalized inverses.In particular, classes of tensor inner, outer, and $(\mathcal{B},\mathcal{C})$ inverses are considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16759 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Perturbation analysis of tensor $(\mathcal{B},\mathcal{C})$-inverse via Einstein product Zhang, Daochang Li, Jingqian Mosic, Dijana Stanimirovic, Predrag S. Functional Analysis Numerical Analysis We investigate the influence of a relatively small perturbation on various generalized inverses functions or quantities derived from a tensor $\mathcal{A}$.When a small tensor perturbation \(\mathcal{E}\) is introduced, it becomes challenging to analyze generalized inverses of the perturbed tensor \( \mathcal{D} =\mathcal{A}+\mathcal{E}\) and to determine how this perturbation affects a generalized inverse of $\mathcal{A}$.Our main goal is to understand the relationship between $\mathcal{D}^\Game$ and \( \mathcal{A}^\Game \), where $(\cdot)^\Game$ denotes a specific generalized inverse or a class of generalized inverses.In particular, classes of tensor inner, outer, and $(\mathcal{B},\mathcal{C})$ inverses are considered. |
| title | Perturbation analysis of tensor $(\mathcal{B},\mathcal{C})$-inverse via Einstein product |
| topic | Functional Analysis Numerical Analysis |
| url | https://arxiv.org/abs/2602.16759 |