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

Chunhong Fu, Jiajia Chen and Qingxiang Xu

Applied Mathematics and Computation, 2021, vol. 399, issue C

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.

Keywords: Sylvester equation; Frobenius norm; Upper bound; Lower bound (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:399:y:2021:i:c:s0096300321000552

DOI: 10.1016/j.amc.2021.126007

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