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Upper bounds and lower bounds for the Frobenius norm of the solution to certain structured Sylvester equation

Author

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  • Fu, Chunhong
  • Chen, Jiajia
  • Xu, Qingxiang

Abstract

This paper studies the Frobenius norm upper bounds and lower bounds of the unique solution to AX+XB=AC+DB, where A∈Cm×m and B∈Cn×n are Hermitian positive definite, and C,D∈Cm×n are arbitrary. Some theoretical improvements of the known results are made. Numerical tests to illustrate the sharpness of the newly obtained upper bounds are dealt with, and numerical examples associated with the positivity of lower bounds are also provided.

Suggested Citation

  • Fu, Chunhong & Chen, Jiajia & Xu, Qingxiang, 2021. "Upper bounds and lower bounds for the Frobenius norm of the solution to certain structured Sylvester equation," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    • Handle: RePEc:eee:apmaco:v:399:y:2021:i:c:s0096300321000552
    DOI: 10.1016/j.amc.2021.126007
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    References listed on IDEAS

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    1. 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.
    2. Liu, Na & Luo, Wei & Xu, Qingxiang, 2018. "New multiplicative perturbation bounds for the generalized polar decomposition," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 259-271.
    3. Zhou, Rong & Wang, Xiang & Tang, Xiao-Bin, 2015. "A generalization of the Hermitian and skew-Hermitian splitting iteration method for solving Sylvester equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 609-617.
    4. Hu, Li-Ying & Guo, Gong-De & Ma, Chang-Feng, 2015. "The least squares anti-bisymmetric solution and the optimal approximation solution for Sylvester equation," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 212-219.
    5. Dehghan, Mehdi & Shirilord, Akbar, 2019. "A generalized modified Hermitian and skew-Hermitian splitting (GMHSS) method for solving complex Sylvester matrix equation," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 632-651.
    Full references (including those not matched with items on IDEAS)

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