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[HTML][HTML] The BiCG algorithm for solving the minimal frobenius norm solution of generalized sylvester tensor equation over the quaternions
M **e, QW Wang, Y Zhang - Symmetry, 2024 - mdpi.com
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 …
tensor equation over quaternions which includes several well-studied matrix/tensor …
The η-anti-Hermitian solution to some classic matrix equations
X Liu - Applied Mathematics and Computation, 2018 - Elsevier
We in this paper consider the η-anti-Hermitian solution to some classic matrix equations AX=
B, AXB= C, AXA η*= B, EXE η*+ FYF η*= H, respectively. We derive the necessary and …
B, AXB= C, AXA η*= B, EXE η*+ FYF η*= H, respectively. We derive the necessary and …
Cramer's Rules of η η-(skew-) Hermitian solutions to the quaternion Sylvester-type matrix equations
Using determinantal representations of the Moore-Penrose inverse previously obtained by
the author within the framework of the theory of quaternion column-row determinants, we first …
the author within the framework of the theory of quaternion column-row determinants, we first …
A constrained system of matrix equations
Sylvester-type matrix equations have wide applications in system science, control theory,
and so on. In this paper, we consider a constrained system of Sylvester-type matrix …
and so on. In this paper, we consider a constrained system of Sylvester-type matrix …
Least squares solution of the quaternion Sylvester tensor equation
QW Wang, X Xu, X Duan - Linear and Multilinear Algebra, 2021 - Taylor & Francis
This paper is concerned with the solution to the least squares problem for the quaternion
Sylvester tensor equation. An iterative algorithm based on tensor format is presented to …
Sylvester tensor equation. An iterative algorithm based on tensor format is presented to …
Efficient iterative method for generalized Sylvester quaternion tensor equation
J Hu, Y Ke, C Ma - Computational and Applied Mathematics, 2023 - Springer
In this study, we employ the biconjugate residual (BCR) algorithm in tensor form to deal with
the generalized Sylvester quaternion tensor equation in order to find the minimum norm …
the generalized Sylvester quaternion tensor equation in order to find the minimum norm …
Explicit formulas and determinantal representation for η-skew-Hermitian solution to a system of quaternion matrix equations
Some necessary and sufficient conditions for the existence of the η-skew-Hermitian solution
quaternion matrix equations the system of matrix equations with η-skew-Hermicity, A1X= C1 …
quaternion matrix equations the system of matrix equations with η-skew-Hermicity, A1X= C1 …
Least squares X=±Xη* solutions to split quaternion matrix equation AXAη*=B
X Liu, Y Zhang - Mathematical Methods in the Applied Sciences, 2020 - Wiley Online Library
In the paper, the split quaternion matrix equation AXA η*= B is considered, where the
operator A η* is the η‐conjugate transpose of A, where η∈{i, j, k}. We propose some new …
operator A η* is the η‐conjugate transpose of A, where η∈{i, j, k}. We propose some new …
Least-squares solutions of generalized Sylvester-type quaternion matrix equations
This paper focuses on finding solutions of generalized Sylvester-type matrix equations over
the quaternion skew-field. We express the general least–squares solutions, and …
the quaternion skew-field. We express the general least–squares solutions, and …