Distance to nearest skew-symmetric matrix polynomials of bounded rank

Andrii Dmytryshyn; Froilán M. Dopico; Rakel Hellberg

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arXiv · 2601.16676

Distance to nearest skew-symmetric matrix polynomials of bounded rank

Andrii Dmytryshyn·Froilán M. Dopico·Rakel Hellberg

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Abstract

We propose an algorithm that approximates a given matrix polynomial of degree $d$ by another skew-symmetric matrix polynomial of a specified rank and degree at most $d$. The algorithm is built on recent advances in the theory of generic eigenstructures and factorizations for skew-symmetric matrix polynomials of bounded rank and degree. Taking into account that the rank of a skew-symmetric matrix polynomial is even, the algorithm works for any prescribed even rank greater than or equal to $2$ and produces a skew-symmetric matrix polynomial of that exact rank. We also adapt the algorithm for matrix pencils to achieve a better performance. Lastly, we present numerical experiments for testing our algorithms and for comparison to the previously known ones.

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Andrii Dmytryshyn, Froilán M. Dopico, Rakel Hellberg. 2026-01-23. Distance to nearest skew-symmetric matrix polynomials of bounded rank. https://arxiv.org/abs/2601.16676

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