An iterative algorithm for the least squares bisymmetric solutions of the matrix equations |
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Authors: | Jing Cai Guoliang Chen |
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Affiliation: | aDepartment of Mathematics, East China Normal University, Shanghai 200062, People’s Republic of China;bSchool of Science, Huzhou Teachers College, Huzhou Zhejiang 313000, People’s Republic of China |
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Abstract: | In this paper, an iterative algorithm is constructed to solve the minimum Frobenius norm residual problem: min over bisymmetric matrices. By this algorithm, for any initial bisymmetric matrix X0, a solution X* can be obtained in finite iteration steps in the absence of roundoff errors, and the solution with least norm can be obtained by choosing a special kind of initial matrix. Furthermore, in the solution set of the above problem, the unique optimal approximation solution to a given matrix in the Frobenius norm can be derived by finding the least norm bisymmetric solution of a new corresponding minimum Frobenius norm problem. Given numerical examples show that the iterative algorithm is quite effective in actual computation. |
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Keywords: | Iterative algorithm Least squares bisymmetric solution Matrix equation Optimal approximation solution |
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