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Abstract
We revisit the notion of root polynomials, thoroughly studied in (Dopico and Noferini, 2020 [9]) for general polynomial matrices, and show how they can efficiently be computed in the case of a matrix pencil λE+A. The method we propose makes extensive use of the staircase algorithm, which is known to compute the left and right minimal indices of the Kronecker structure of the pencil. In addition, we show here that the staircase algorithm, applied to the expansion (λ−λ0)E+(A−λ0E), constructs a block triangular pencil from which a minimal basis and a maximal set of root polynomials at the eigenvalue λ0, can be computed in an efficient manner.
Original language | English |
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Pages (from-to) | 86-115 |
Number of pages | 30 |
Journal | Linear Algebra and Its Applications |
Volume | 658 |
DOIs | |
Publication status | Published - 1 Feb 2023 |
MoE publication type | A1 Journal article-refereed |
Keywords
- Local Smith form
- Matrix pencil
- Maximal set
- Minimal basis
- Root polynomial
- Smith form
- Staircase algorithm
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Dive into the research topics of 'On computing root polynomials and minimal bases of matrix pencils'. Together they form a unique fingerprint.Projects
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Noferini_Vanni_AoF_Project: Noferini Vanni Academy Project
Noferini, V. (Principal investigator), Quintana Ponce, M. (Project Member), Barbarino, G. (Project Member), Wood, R. (Project Member) & Nyman, L. (Project Member)
01/09/2020 → 31/08/2024
Project: Academy of Finland: Other research funding