Solving the QLY Least Squares Problem of Dual Quaternion Matrix Equation Based on STP of Dual Quaternion Matrices

Abstract

Dual algebra plays an important role in kinematic synthesis and dynamic analysis, but there are still few studies on dual quaternion matrix theory. This paper provides an efficient method for solving the QLY least squares problem of the dual quaternion matrix equation AXB+CYD≈E, where X, Y are unknown dual quaternion matrices with special structures. First, we define a semi-tensor product of dual quaternion matrices and study its properties, which can be used to achieve the equivalent form of the dual quaternion matrix equation. Then, by using the dual representation of dual quaternion and the GH-representation of special dual quaternion matrices, we study the expression of QLY least squares Hermitian solution of the dual quaternion matrix equation AXB+CYD≈E. The algorithm is given and the numerical examples are provided to illustrate the efficiency of the method.

Keywords

• dual quaternion matrix equation
• QLY least squares problem
• semi-tensor product of dual quaternion matrices
• dual representation
• GH -representation%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <named-content content-type="inline"><inline-formula> <mml:math id="mm2222"> <mml:semantics> <mml:mi mathvariant="script">GH</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-representation