Matrix LSQR algorithm for structured solutions to quaternionic least squares problem.

In this paper, we employ matrix LSQR algorithm to deal with quaternionic least squares problem in order to find the minimum norm solutions with kinds of special structures, and propose a strategy to accelerate convergence rate of the algorithm via right–left preconditioning of the coefficient matrices. We mainly focus on analyzing the minimum norm η-Hermitian solution and the minimum norm η-biHermitian solution to the quaternionic least squares problem, η∈{i,j,k}. Other structured solutions also can be obtained using the proposed technique. A number of numerical experiments are performed to show the efficiency of the preconditioned matrix LSQR algorithm.