Least-Squares Solutions of Generalized Sylvester-Type Quaternion Matrix Equations
Advances in Applied Clifford Algebras, cilt.33, sa.3, 2023 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 33 Sayı: 3
- Basım Tarihi: 2023
- Doi Numarası: 10.1007/s00006-023-01276-w
- Dergi Adı: Advances in Applied Clifford Algebras
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH
- Anahtar Kelimeler: Sylvester quaternion matrix equations, Least-squares problem, Perhermitian, Skew-perhermitian, Color image restoration
- Kırklareli Üniversitesi Adresli: Evet
Özet
This paper focuses on finding solutions of generalized Sylvester-type matrix equations over the quaternion skew-field. We express the general least–squares solutions, and perhermitian, skew-perhermitian least-squares solutions of AXB+ CYD= E and AXB+ CXD= E over the quaternion skew-field in terms of a vec operator (defined specifically for matrices over the quaternion skew-field) and the Moore–Penrose pseudoinverse. In addition, characterizations that facilitate the computation of the least-squares solutions closest to prescribed quaternion matrices are deduced. We illustrate our theoretical findings on several numerical examples, most of which originate from color image restoration via Tikhonov regularization.