Minimum-norm least-squares solutions of generalized Sylvester-type quaternion matrix equation with bi-Hermitian and skew bi-Hermitian constraints

Sinem Şimşek; Tuğba Demirkol; Yıldız Kulaç; Halim Özdemir; Sinem Şimşek; Tuğba Demirkol; Yıldız Kulaç; Halim Özdemir

doi:10.3934/math.2026380

AIMS Mathematics

2026, Volume 11, Issue 4: 9210-9227. doi: 10.3934/math.2026380

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Research article

Minimum-norm least-squares solutions of generalized Sylvester-type quaternion matrix equation with bi-Hermitian and skew bi-Hermitian constraints

1.
Department of Mathematics, Faculty of Arts and Sciences, Kırklareli University, Kırklareli 39100, Turkey
2.
Department of Mathematics, Faculty of Science, Sakarya University, Sakarya 54050, Turkey

Received: 30 December 2025 Revised: 11 March 2026 Accepted: 23 March 2026 Published: 03 April 2026
MSC : 15A06, 15A09, 15A24, 15B33, 15B57

This paper investigated minimum-norm least-squares solutions to the quaternion matrix equation $ KXL+MYN = O $, where the unknown matrices $ X $ and $ Y $ were subject to bi-Hermitian or skew bi-Hermitian constraints. Building on the derived theoretical results, an explicit numerical algorithm was proposed. Moreover, several numerical examples were presented to validate the accuracy of these results.
- quaternion matrix equations,
- real matrix representation,
- minimum norm least-squares solutions,
- bi-Hermitian solutions,
- skew bi-Hermitian solutions
Citation: Sinem Şimşek, Tuğba Demirkol, Yıldız Kulaç, Halim Özdemir. Minimum-norm least-squares solutions of generalized Sylvester-type quaternion matrix equation with bi-Hermitian and skew bi-Hermitian constraints[J]. AIMS Mathematics, 2026, 11(4): 9210-9227. doi: 10.3934/math.2026380

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Abstract

This paper investigated minimum-norm least-squares solutions to the quaternion matrix equation $ KXL+MYN = O $, where the unknown matrices $ X $ and $ Y $ were subject to bi-Hermitian or skew bi-Hermitian constraints. Building on the derived theoretical results, an explicit numerical algorithm was proposed. Moreover, several numerical examples were presented to validate the accuracy of these results.

References

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