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Your search keyword '"Anli Wei"' showing total 3 results
Start Over Author "Anli Wei" Topic least squares
3 results on '"Anli Wei"'

1. A new method based on semi-tensor product of matrices for solving reduced biquaternion matrix equation l/Σ/p=1 ApXBp = C and its application in color image restoration.

Author

Jianhua Sun, Ying Li, Mingcui Zhang, Zhihong Liu, and Anli Wei

Subjects
COLOR image processing, MATRICES (Mathematics), LINEAR equations, LEAST squares, QUATERNIONS
Abstract

In this paper, semi-tensor product of real matrices is extended to reduced biquaternion matrices, and then some new conclusions of the reduced biquaternion matrices under the vector operator are proposed using semi-tensor product of reduced biquaternion matrices, so that the reduced biquaternion matrix equation l/Σ/p=1 ApXBp = C can be transformed into a reduced biquaternion linear equations, then the expression of the least squares solution of the equation is obtained using the LC-representation and MoorePenrose inverse. The necessary and sufficient conditions for the compatibility and the expression of general solutions of the equation are obtained, and the minimal norm solutions are also given. Finally, our proposed method of solving the reduced biquaternion matrix equation is applied to color image restoration. [ABSTRACT FROM AUTHOR]

Published
2023
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2. Constrainted least squares solution of Sylvester equation

Author

Ying Li, Wenxv Ding, Anli Wei, and Dong Wang

Subjects
Matrix (mathematics), Product (mathematics), ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Quaternion matrix, MathematicsofComputing_NUMERICALANALYSIS, Applied mathematics, Inverse, Quaternion, Representation (mathematics), Sylvester equation, Least squares, Mathematics
Abstract

In this paper, we study several constrainted least squares solutions of quaternion Sylvester matrix equation. We first propose a real vector representation of quaternion matrix and study its properties. By using this real vector representation, semi-tensor product of matrices, swap matrix and Moore-Penrose inverse, we derive compatible conditions and the expressions of several constrainted least squares solutions of quaternion Sylvester equation.

Published
2021

3. Special arrowhead least squares solution of the quaternion generalized Sylvester matrix equation

Author

Dong Wang, Wenxv Ding, Anli Wei, and Ying Li

Subjects
Algebra, Mathematical model, Computation, Product (mathematics), ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, MathematicsofComputing_NUMERICALANALYSIS, Inverse, Quaternion, Representation (mathematics), Least squares, Hermitian matrix, Mathematics
Abstract

In this paper, we study special arrowhead solution of the quaternion generalized Sylvester matrix equation by using semi-tensor product of matrices. We first propose a real vector representation of quaternion matrix and study its properties. By means of this real vector representation, semi-tensor product of matrices and Moore-Penrose inverse, we solve the least squares arrowhead Hermitian (skew-Hermitian) problem of the quaternion generalized Sylvester matrix equation. The expressions of these solutions only involve real arithmetic, which makes the procedure computation more flexible and efficient.

Published
2021

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