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Abstract: By means of complex representation of a quaternion matrix, we study the relationship between the solutions of the quaternion equality constrained least squares problem and that of complex equality constrained least squares problem, and obtain a new technique of finding a solution of the quaternion equality constrained least squares problem. [Copyright &y& Elsevier]

Abstract: In this paper, we first present a class of structure-oriented hybrid two-stage iteration methods for solving the large and sparse blocked system of linear equations, as well as the saddle point problem as a special case. And the new methods converge to the solution under suitable restrictions, for instance, when the coefficient matrix is positive stable matrix generally. Numerical experiments for a model generalized saddle point problem are given, and the results show that our new methods are feasible and efficient, and converge faster than the Classical Uzawa Method. [Copyright &y& Elsevier]

Abstract In this paper, we study the power method of the right eigenvalue problem of a quaternion matrix A. If A is Hermitian, we propose the power method that is a direct generalization of that of complex Hermitian matrix. When A is non-Hermitian, by applying the properties of quaternion right eigenvalues, we propose the power method for computing the standard right eigenvalue with the maximum norm and the associated eigenvector. We also briefly discuss the inverse power method and shift inverse power method for the both cases. The real structure-preserving algorithm of the power method in the two cases are also proposed, and numerical examples are provided to illustrate the efficiency of the proposed power method and inverse power method. [ABSTRACT FROM AUTHOR]

In this paper, we put forward a new structure-preserving algorithm based on the semi-tensor product of matrices for the split quaternion matrix LDU decomposition, which makes full use of high-level operations, and relation of operations between split quaternion matrices and their L -representation matrices. The algorithm is more stable and efficient than the complex structure-preserving algorithm proposed in Wang et al. (2021). Numerical experiments are provided to verify the efficiency of the new structure-preserving algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we survey three different forms of Householder based transformations for quaternion matrices in the literature, and propose a new form of quaternion Householder based transformation. We propose real structure-preserving algorithms of these Householder based transformations, which make the procedure computationally more flexible and efficient. We compare the computation counts and assignment numbers of these algorithms. We also compare the effectiveness of these real structure-preserving algorithms applying to the quaternion QRD and the quaternion SVD. All these four real structure-preserving algorithms are more efficient, comparing to the algorithms which apply Quaternion Toolbox using quaternion arithmetics, or algorithms which directly performs real Householder transformations on the real representation of a quaternion matrix. Among these four real structure-preserving algorithms, the most efficient ones are based on quaternion Householder reflection, and new proposed Householder based transformation. [ABSTRACT FROM AUTHOR]

Abstract: The nonhomogeneous Yakubovich-transpose matrix equation , which contains the well-known Kalman–Yakubovich-transpose matrix equation and general discrete Lyapunov-transpose matrix equation as special cases, has many important applications in control system theory. This study presents two methods to obtain the closed-form solutions of the nonhomogeneous Yakubovich-transpose matrix equation. Moreover, the equivalent forms of the solutions are provided and one of the solutions is established with the controllability matrix, the observability matrix and symmetric operator matrix. [Copyright &y& Elsevier]