On accurate error estimates for the quaternion least squares and weighted least squares problems

摘要

ABSTRACT In this paper, we study error estimates of the quaternion least squares problem and the quaternion weighted least squares problem. For different cases, we define different condition numbers and effective condition numbers. We propose upper bounds of absolute and relative errors of the minimal norm LS solution and the general LS solution of the quaternion least squares problem and the quaternion weighted least squares problem, respectively, by using different condition numbers and effective condition numbers to make error estimates sharper.