Combinatorics of polynomial chains

In this paper we consider two polynomial chains and we study the existence of an intermediate polynomial chain satisfying interlacing inequality relations together with some convexity-like properties that arise from applications in completion problems. The presented result is a vast generalisation o...

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Bibliographic Details
Published in:Linear algebra and its applications 2020-03, Vol.589, p.130-157
Main Authors: Dodig, Marija, Stošić, Marko
Format: Article
Language:English
Subjects:
Completion of matrix pencils
Convexity
Polynomial chains
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Summary:In this paper we consider two polynomial chains and we study the existence of an intermediate polynomial chain satisfying interlacing inequality relations together with some convexity-like properties that arise from applications in completion problems. The presented result is a vast generalisation of existing results dealing with intermediate polynomial chains. The proof of the main result is completely novel to the field, different from all the existing methods used in similar problems. The obtained necessary and sufficient conditions are simple, explicit and constructive.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2019.12.028