A new technique of quaternion equality constrained least squares problem

Abstract

By means of complex representation of a quaternion matrix, we study the relationship between the solutions of the quaternion equality constrained least squares problem and that of complex equality constrained least squares problem, and obtain a new technique of finding a solution of the quaternion equality constrained least squares problem.

Algebraic methods for equality constrained least squares problems in commutative quaternionic theory

“…In other four-dimensional Clifford algebras, many scholars have studied these kinds of problems. [17][18][19][20][21][22][23] Jiang et al 20,21 studied the quaternion LSE problems by using GSVD and the complex representation of a quaternion matrix, discussed the relationship between the solutions of quaternion LSE problems and the solutions of complex LSE problems, and derived the algorithms for solving quaternion LSE problems. Li et al 22 proposed a real structure-preserving algorithm by using the special structure of the real representation of a quaternion matrix, thus obtaining the solution of quaternion LSE problems.…”

Real structure‐preserving algorithm for quaternion equality constrained least squares problem

“…In the process of studying the theory and numerical calculation of these mathematical and physical problems, it is often necessary to solve the approximate solutions of linear quaternion systems, namely, the quaternion least squares problems. As an extremely effective research tool of quaternion quantum mechanics and quantum field theory, the quaternion least squares problems have attracted extensive attention in the field of mathematical physics . In addition, the quaternion least squares problems have important applications in biology, electricity, vibration theory, structure design, automatic control theory, and optimal control …”

“…For example, in Jiang and Wei, by using complex representation of quaternion matrices, the authors give the necessary and sufficient condition for existence of solution of QLSE problem. In Jiang et al, the authors study the relationship between the solutions of the QLSE problem and those of complex equality constrained least squares (LSE) problem, and obtain a new technique to find solutions of QLSE problem. For more results, see Jiang and Wei and Jiang et al and their literatures.…”

“…As an extremely effective research tool of quaternion quantum mechanics and quantum field theory, the quaternion least squares problems have attracted extensive attention in the field of mathematical physics. [2][3][4][5][6][7][8][9][10] In addition, the quaternion least squares problems have important applications in biology, electricity, vibration theory, structure design, automatic control theory, and optimal control. 2,3,[11][12][13][14][15][16] The computation of the quaternion least squares problems is extremely complex.…”

“…In Jiang et al, 9 the authors study the relationship between the solutions of the QLSE problem and those of complex equality constrained least squares (LSE) problem, and obtain a new technique to find solutions of QLSE problem. For more results, see Jiang and Wei 8 and Jiang et al 9 and their literatures. In this paper, our goal is to find an effective computation method of the QLSE problem.…”