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Conjugate gradient-like algorithms for constrained operator equation related to quadratic inverse eigenvalue problems

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Abstract

As is well known, linear operator equations have wide applications in many areas of engineering and applied mathematics. In the present paper, we are interested in solving the linear operator equation

$$\begin{aligned} {\mathscr {F}}(J)+{\mathscr {G}}(K)+{\mathscr {H}}(L)=N, \end{aligned}$$

where J, K and L should be partially bisymmetric under a prescribed submatrix constraint. Three conjugate gradient-like algorithms are derived for solving this constrained operator equation including the Lyapunov, Stein and Sylvester matrix equations and the quadratic inverse eigenvalue problem as special cases. The algorithms converge to the solutions of the linear operator equation within a finite number of iterations in the absence of round-off errors. At the end, the accuracy and efficiency of the introduced algorithms are demonstrated numerically with three examples.

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Acknowledgements

The author would like to thank the editor and the anonymous reviewers for their valuable comments and careful reading of the original manuscript which substantially improved the quality and presentation of this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

    Masoud Hajarian

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  1. Masoud Hajarian
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Correspondence to Masoud Hajarian.

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Communicated by Andreas Fischer.

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Hajarian, M. Conjugate gradient-like algorithms for constrained operator equation related to quadratic inverse eigenvalue problems. Comp. Appl. Math. 40, 137 (2021). https://doi.org/10.1007/s40314-021-01523-5

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