Hermitian tridiagonal solution with the least norm to quaternionic least squares problem
Quaternionic least squares (QLS) is ail efficient method for solving approximate problems in quaternionic quantum theory. In view of the extensive applications of Hermitian tridiagonal matrices in physics, in this paper we list some properties of basis matrices and subvectors related to tridiagonal matrices, and give ail iterative algorithm for finding Hermitian tridiagonal solution with the least norm to the quaternionic least squares problem by making the best use of structure of real representation matrices, we also propose a preconditioning strategy for the Algorithm LSQR-Q in Wang, Wei and Feng (2008) [14] and our algorithm. Numerical experiments are provided to verify the effectiveness of our method. (C) 2009 Elsevier B.V. All rights reserved.
quaternionic least squares preconditioning quaternion matrix hermitian tridiagonal matrix lsqr