The Minimum-Norm Least Squares Solutions to Quaternion Tensor Systems

Abstract

In this paper, we investigate the minimum-norm least squares solution to a quaternion tensor system A1*NX1=C1,A1*NX2+A2*NX3=C2,E1*NX1*MF1+E1*NX2*MF2+E2*NX3*MF2=D by using the Moore–Penrose inverses of block tensors. As an application, we discuss the quaternion tensor system A*NX=C,E*NX*MF=D for minimum-norm least squares reducible solutions. To illustrate the results, we present an algorithm and a numerical example.

Keywords

• quaternion tensor equation
• least squares (reducible) solution
• minimum norm
• Moore–Penrose inverse