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Least Squares Solution of the Linear Operator Equation

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  • Masoud Hajarian

    (Shahid Beheshti University)

Abstract

The least squares problems have wide applications in inverse Sturm–Liouville problem, particle physics and geology, inverse problems of vibration theory, control theory, digital image and signal processing. In this paper, we discuss the solution of the operator least squares problem. By extending the conjugate gradient least squares method, we propose an efficient matrix algorithm for solving the operator least squares problem. The matrix algorithm can find the solution of the problem within a finite number of iterations in the absence of round-off errors. Some numerical examples are given to illustrate the effectiveness of the matrix algorithm.

Suggested Citation

  • Masoud Hajarian, 2016. "Least Squares Solution of the Linear Operator Equation," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 205-219, July.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:1:d:10.1007_s10957-015-0737-5
    DOI: 10.1007/s10957-015-0737-5
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    1. repec:taf:tsysxx:v:46:y:2015:i:3:p:488-502 is not listed on IDEAS
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    Cited by:

    1. Hu, Jingjing & Ma, Changfeng, 2018. "Conjugate gradient least squares algorithm for solving the generalized coupled Sylvester-conjugate matrix equations," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 174-191.
    2. Huang, Baohua & Ma, Changfeng, 2018. "An iterative algorithm for the least Frobenius norm least squares solution of a class of generalized coupled Sylvester-transpose linear matrix equations," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 58-74.
    3. Qu, Hongli & Xie, Dongxiu & Xu, Jie, 2021. "A numerical method on the mixed solution of matrix equation ∑i=1tAiXiBi=E with sub-matrix constraints and its application," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    4. Baohua Huang & Changfeng Ma, 2019. "The least squares solution of a class of generalized Sylvester-transpose matrix equations with the norm inequality constraint," Journal of Global Optimization, Springer, vol. 73(1), pages 193-221, January.

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