New multiplicative perturbation bounds for the generalized polar decomposition
Na Liu, Wei Luo, Qingxiang Xu
TL;DR
This paper introduces new Frobenius norm bounds for structured Sylvester equations and uses them to derive improved multiplicative perturbation bounds for polar decompositions, enhancing previous results.
Contribution
The paper presents novel Frobenius norm bounds for Sylvester equations and applies them to obtain improved perturbation bounds for polar factors.
Findings
New Frobenius norm bounds for Sylvester equations
Enhanced multiplicative perturbation bounds for polar factors
Improved previous perturbation results
Abstract
Some new Frobenius norm bounds of the unique solution to certain structured Sylvester equation are derived. Based on the derived norm upper bounds, new multiplicative perturbation bounds are provided both for subunitary polar factors and positive semi-definite polar factors. Some previous results are then improved.
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Taxonomy
TopicsMatrix Theory and Algorithms · Satellite Communication Systems · Inertial Sensor and Navigation