Least squares X=±Xη* solutions to split quaternion matrix equation AXAη*=B
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DOI: 10.1002/mma.6033
Abstract: In the paper, the split quaternion matrix equation AXAη*=B is considered, where the operator Aη* is the η‐conjugate transpose of A, where η∈{i,j,k}. We propose some new real representations, which well exploited the special structures… read more here.
Keywords: least squares; matrix equation; equation; quaternion matrix ... See more keywords
The use of homotopy analysis method for solving generalized Sylvester matrix equation with applications
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DOI: 10.1007/s00366-020-01219-0
Abstract: In this research, we introduce and analyze homotopy analysis method (HAM) for solving approximately linear matrix equation $$ \sum \limits \limits _{i=1}^{s}A_iXB_i+C=\mathbf{0} $$ , where $$ A_i,\;B_i \;(i=1,\ldots ,s), \; C \in \mathbb {C}^{n \times… read more here.
Keywords: matrix equation; homotopy analysis; method; analysis method ... See more keywords
An iterative algorithm for solving the generalized Sylvester-conjugate matrix equation
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DOI: 10.1007/s12190-017-1156-6
Abstract: This paper aims to extend the conjugate gradient least squares method to solve the least squares problem of the generalized Sylvester-conjugate matrix equation. For any initial values, the proposed iterative method can obtain the least… read more here.
Keywords: conjugate matrix; algorithm; iterative algorithm; matrix equation ... See more keywords
Completion of Symmetric Orthogonal Matrices and Corresponding Matrix Equation Problem
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DOI: 10.1007/s40819-018-0530-x
Abstract: The completion problem for symmetric orthogonal matrix and corresponding matrix equation problem are studied. We give some necessary and sufficient conditions of solvability and the expressions of solutions. In addition, in the solution set of… read more here.
Keywords: matrix equation; corresponding matrix; symmetric orthogonal; equation problem ... See more keywords
Solvability for a Nonlinear Matrix Equation
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DOI: 10.1007/s41980-018-0080-3
Abstract: In this paper, the matrix equation $$X+\sum _{i=1}^{m}A_{i}^*X^{-q_{i}}A_{i}=I$$X+∑i=1mAi∗X-qiAi=I with $$0 read more here.
Keywords: matrix equation; equation; nonlinear matrix; solvability nonlinear ... See more keywords
A novel iterative method for the solution of a nonlinear matrix equation
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DOI: 10.1016/j.apnum.2020.03.012
Abstract: Abstract This paper provides a novel inversion free variant of the fixed point iteration strategy to obtain a maximal positive definite solution for the nonlinear matrix equation X + A ⁎ X − 1 A… read more here.
Keywords: matrix equation; solution nonlinear; nonlinear matrix; method ... See more keywords
On commuting solutions of the Yang–Baxter-like matrix equation
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DOI: 10.1016/j.jmaa.2018.02.030
Abstract: Abstract Let A be an arbitrary square matrix and its Jordan canonical form is P − 1 A P = J = diag ( J 1 ( λ 1 ) , ⋯ , J q… read more here.
Keywords: baxter like; solutions yang; matrix equation; yang baxter ... See more keywords
On the investigation of activation functions in gradient neural network for online solving linear matrix equation
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DOI: 10.1016/j.neucom.2020.06.097
Abstract: Abstract In this paper, we investigate different activation functions (AFs) on convergence performance of a gradient-based neural network (GNN) for solving linear matrix equation, AXB + X = C . It is observed that, by… read more here.
Keywords: matrix equation; power; linear matrix; convergence ... See more keywords
An efficient real representation method for least squares problem of the quaternion constrained matrix equation AXB + CY D = E
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DOI: 10.1080/00207160.2020.1821001
Abstract: Let and represent the sets of all η-Hermitian quaternion matrices and η-anti-Hermitian quaternion matrices, respectively. On the basis of the real representation matrix of a quaternion matrix and its particular structure, we convert the least… read more here.
Keywords: quaternion; squares problem; matrix equation; least squares ... See more keywords
ZNNs With a Varying-Parameter Design Formula for Dynamic Sylvester Quaternion Matrix Equation.
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DOI: 10.1109/tnnls.2022.3163293
Abstract: This article aims to studying how to solve dynamic Sylvester quaternion matrix equation (DSQME) using the neural dynamic method. In order to solve the DSQME, the complex representation method is first adopted to derive the… read more here.
Keywords: sylvester quaternion; dynamic sylvester; model; dvpznn ... See more keywords
The Feasibility of Homotopy Continuation Method for a Nonlinear Matrix Equation
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DOI: 10.1155/2020/1787058
Abstract: In this paper, we discuss the feasibility of homotopy continuation method for the nonlinear matrix equations with . This iterative method does not depend on a good initial approximation to the solution of matrix equation. read more here.
Keywords: homotopy continuation; nonlinear matrix; matrix equation; continuation method ... See more keywords