Structure Preserving Quaternion Biconjugate Gradient Method

.This paper considers a novel structure-preserving method for solving non-Hermitian quaternion linear systems arising from color image deblurred problems. From the quaternion Lanczos biorthogonalization procedure that preserves the quaternion tridiagonal form at each iteration, we derive the quaternion biconjugate gradient method for solving the linear systems and then establish the convergence analysis of the proposed algorithm. Finally, we provide some numerical examples to illustrate the feasibility and validity of our method in comparison with the QGMRES, especially in terms of computing time.Keywordsquaternion linear systemsquaternion Lanczos biorthogonalization procedurequaternion biconjugate gradient methodcolor image deblurringMSC codes15B3365F1094A08