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The BiCG Algorithm for Solving the Minimal Frobenius Norm Solution of Generalized Sylvester Tensor Equation over the Quaternions.
- Source :
- Symmetry (20738994); Sep2024, Vol. 16 Issue 9, p1167, 22p
- Publication Year :
- 2024
-
Abstract
- In this paper, we develop an effective iterative algorithm to solve a generalized Sylvester tensor equation over quaternions which includes several well-studied matrix/tensor equations as special cases. We discuss the convergence of this algorithm within a finite number of iterations, assuming negligible round-off errors for any initial tensor. Moreover, we demonstrate the unique minimal Frobenius norm solution achievable by selecting specific types of initial tensors. Additionally, numerical examples are presented to illustrate the practicality and validity of our proposed algorithm. These examples include demonstrating the algorithm's effectiveness in addressing three-dimensional microscopic heat transport and color video restoration problems. [ABSTRACT FROM AUTHOR]
- Subjects :
- SYLVESTER matrix equations
QUATERNIONS
EQUATIONS
ALGORITHMS
VIDEOS
Subjects
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 16
- Issue :
- 9
- Database :
- Complementary Index
- Journal :
- Symmetry (20738994)
- Publication Type :
- Academic Journal
- Accession number :
- 180009472
- Full Text :
- https://doi.org/10.3390/sym16091167