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AIMS Mathematics

2022, Volume 7, Issue 2: 1845-1855. doi: 10.3934/math.2022106
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Research article

Double iterative algorithm for solving different constrained solutions of multivariate quadratic matrix equations

  • Department of science, Shandong Jianzhu University, Jinan 250101, China
  • Received: 05 August 2021 Accepted: 20 October 2021 Published: 03 November 2021

  • MSC : 15A24, 65F45, 65H10

  • Constrained solutions are required in some practical problems. This paper studies the problem of different constrained solutions for a class of multivariate quadratic matrix equations, which has rarely been studied before. First, the quadratic matrix equations are transformed into linear matrix equations by Newton's method. Second, the different constrained solutions of the linear matrix equations are solved by the modified conjugate gradient method, and then the different constrained solutions of the multivariate quadratic matrix equations are obtained. Finally, the convergence of the algorithm is proved. The algorithm can be well performed on the computers, and the effectiveness of the method is verified by numerical examples.

    Citation: Shousheng Zhu. Double iterative algorithm for solving different constrained solutions of multivariate quadratic matrix equations[J]. AIMS Mathematics, 2022, 7(2): 1845-1855. doi: 10.3934/math.2022106

    Related Papers:

  • Constrained solutions are required in some practical problems. This paper studies the problem of different constrained solutions for a class of multivariate quadratic matrix equations, which has rarely been studied before. First, the quadratic matrix equations are transformed into linear matrix equations by Newton's method. Second, the different constrained solutions of the linear matrix equations are solved by the modified conjugate gradient method, and then the different constrained solutions of the multivariate quadratic matrix equations are obtained. Finally, the convergence of the algorithm is proved. The algorithm can be well performed on the computers, and the effectiveness of the method is verified by numerical examples.


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