4.7 Article

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

Journal

APPLIED MATHEMATICS AND COMPUTATION
Volume 399, Issue -, Pages -

Publisher

ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2021.126007

Keywords

Sylvester equation; Frobenius norm; Upper bound; Lower bound

Funding

  1. National Natural Science Foundation of China [11671261,11971136]
  2. Science and Technology Commission of Shanghai Municipality [18590745200]

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This paper studies the Frobenius norm upper bounds and lower bounds of the unique solution to AX + XB = AC + DB, with improvements made to known results. Numerical tests demonstrate the sharpness of the newly obtained upper bounds, and numerical examples associated with the positivity of lower bounds are provided.
This paper studies the Frobenius norm upper bounds and lower bounds of the unique solution to AX + XB = AC + DB, where A is an element of C-mxm and B is an element of C-nxn are Hermitian positive definite, and C, D is an element of C-mxn 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. (C) 2021 Elsevier Inc. All rights reserved.

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