QR decomposition of dual matrices and its application

Abstract

Dual number matrix decompositions have played an important role in fields such as kinematics and computer graphics in recent years. In this paper, we present a QR decomposition algorithm for dual number matrices. When dealing with large-scale problems, we present the thin QR decomposition of dual number matrices, along with its algorithm with column pivoting. In numerical experiments, we discuss the suitability of different QR algorithms when confronted with various large-scale dual matrices, providing their respective domains of applicability. Finally, we employ the QR decomposition of dual matrices to compute the DMPGI, attaining results of higher precision.