.png){kind=icon}
Return
Projection-based iterative methods for solving multilinear systems
.png){kind=icon}
PRE
AI
DOI：10.1007/s40314-026-03774-6.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
The computational challenges inherent in multilinear systems present significant obstacles in contemporary engineering and scientific applications, where traditional matrix-based iterative approaches are inadequate for computing tensor inverses and solving multilinear equations. This study addresses these limitations by explicitly developing novel projection-based iterative methodologies for multilinear systems within the context of the t-product, including tensor-based implementations of the biconjugate gradient method, the squared conjugate gradient method, and the stabilized biconjugate gradient method. An innovative tensor-based iterative representation is introduced to compute the Moore–Penrose inverse of tensors, accompanied by the design of efficient and robust computational algorithms for these methodologies via the t-product. The computational efficiency and practical advantages of these approaches are validated by a few numerical examples. In addition, an application is demonstrated to solve color image restoration problems.
Keywords:
Tensor
t-product
Moore–Penrose inverse
Multilinear systems
Image deblurring
Journal
C
IF:
0
Papers:
266
Citations:
0
Organization
Cited Papers
.png){kind=icon}
ShareSaveShareSaveShareSaveShareSaveShareSavePolar $n$-Complex and $n$-Bicomplex Singular Value Decomposition and Principal Component Pursuit
OAAI
OAAIShareSave
View more