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PreprintCC BY 4.0arXiv

Generic factorizations and alternating direction method for fixed-rank approximation of matrix polynomials

  • Sweta Das
  • Andrii Dmytryshyn
  • Froilán M. Dopico
  • Mårten Gulliksson
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Abstract

We present an algorithm for approximating a given matrix polynomial of degree d by a matrix polynomial of prescribed rank and degree at most d. The method builds on recent advances in the theory of generic eigenstructures and factorizations of matrix polynomials with bounded rank and degree. We also give a specialized treatment of the case of matrix pencils (degree one matrix polynomials), motivated by its particular theoretical and practical importance. Lastly, numerical experiments are reported to assess the performance of the proposed approach and to compare it with existing methods.

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Cite

BibTeXRIS
BibTeX
@misc{das2026generic,
  title = {{Generic factorizations and alternating direction method for fixed-rank approximation of matrix polynomials}},
  author = {Sweta Das and Andrii Dmytryshyn and Froilán M. Dopico and Mårten Gulliksson},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04799},
  eprint = {2611.04799},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04799},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Generic factorizations and alternating direction method for fixed-rank approximation of matrix polynomials
AU  - Sweta Das
AU  - Andrii Dmytryshyn
AU  - Froilán M. Dopico
AU  - Mårten Gulliksson
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04799
UR  - https://arxiv.org/abs/2611.04799
AB  - We present an algorithm for approximating a given matrix polynomial of degree d by a matrix polynomial of prescribed rank and degree at most d. The method builds on recent advances in the theory of generic eigenstructures and factorizations of matrix polynomials with bounded rank and degree. We also give a specialized treatment of the case of matrix pencils (degree one matrix polynomials), motivated by its particular theoretical and practical importance. Lastly, numerical experiments are reported to assess the performance of the proposed approach and to compare it with existing methods.
ER  -