Algebraic techniques for least squares problems in commutative quaternionic theory. (20th January 2020)

• Record Type: Journal Article
• Authors: Zhang, Dong; Guo, Zhenwei; Wang, Gang; Jiang, Tongsong
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 6(2020)
• Page Start: 3513
• Page End: 3523
• Publication Date: 2020-01-20
• Subjects: commutative quaternion -- complex representation -- least squares problem -- matrix norm -- real representation; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6135
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : Due to the rise of commutative quaternion in Hopfield neural networks, digital signal, and image processing, one encounters the approximate solution problems of the commutative quaternion linear equations A X ≈ B and A X C ≈ B . This paper, by means of real representation and complex representation of commutative quaternion matrices, introduces concepts of norms of commutative quaternion matrices and derives two algebraic techniques for finding solutions of least squares problems in commutative quaternionic theory.