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A shift-splitting hierarchical identification iterative algorithm for solving the matrix equation AX−X‾B=C

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Veröffentlicht in:Advances in Continuous and Discrete Models vol. 2025, no. 1 (Dec 2025), p. 97
Veröffentlicht:
Springer Nature B.V.
Schlagworte:
Exact solutions
Iterative algorithms
Splitting
Iterative methods
Ramadan
Algorithms
Identification
Education
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Abstract:Based on the Hermitian and skew Hermitian splitting of the coefficient matrices, we demonstrate a shift-splitting hierarchical identification (SSHI) iterative algorithm to solve the matrix equation AX−X‾B=C<inline-graphic specific-use="web" mime-subtype="GIF" xlink:href="13662_2024_3849_Article_IEq1.gif" />. For any initial value, the suggested method converges to the exact solution under certain conditions. Three numerical examples are presented to demonstrate the effectiveness of the shift-splitting hierarchical identification (SSHI) iterative method and to compare it to the Jacobi-gradient iterative algorithm (JGI) (Bayoumi in Appl. Math. Inf. Sci. (2021)) and the gradient iterative algorithm (GI).
ISSN:1687-1839
1687-1847
DOI:10.1186/s13662-024-03849-w
Quelle:Advanced Technologies & Aerospace Database