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Abstract
We define a compact local Smith–McMillan form of a rational matrix (Formula presented.) as the diagonal matrix whose diagonal elements are the nonzero entries of a local SmithMcMillan form of (Formula presented.). We show that a recursive rank search procedure, applied to a blockToeplitz matrix built on the Laurent expansion of (Formula presented.) around an arbitrary complex point (Formula presented.), allows us to compute a compact local SmithMcMillan form of that rational matrix (Formula presented.) at the point (Formula presented.), provided we keep track of the transformation matrices used in the rank search. It also allows us to recover the root polynomials of a polynomial matrix and root vectors of a rational matrix, at an expansion point (Formula presented.). Numerical tests illustrate the promising performance of the resulting algorithm.
Original language  English 

Number of pages  17 
Journal  LINEAR AND MULTILINEAR ALGEBRA 
DOIs  
Publication status  Epub ahead of print  15 Apr 2024 
MoE publication type  A1 Journal articlerefereed 
Keywords
 compact local Smith–McMillan form
 Laurent expansion
 rational matrix
 Smith–McMillan form
 Toeplitz search
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Noferini_Vanni_AoF_Project: Noferini Vanni Academy Project
Noferini, V., Quintana Ponce, M., Barbarino, G., Wood, R., Nyman, L. & Mahamud, S.
01/09/2020 → 31/08/2024
Project: Academy of Finland: Other research funding