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

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.

Automated summary

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.