Structure preserving quaternion full orthogonalization method with applications |
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Authors: | Tao Li Qing-Wen Wang |
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Affiliation: | 1. Department of Mathematics, Key Laboratory of Engineering Modeling and Statistical Computation of Hainan Province, Hainan University, Haikou, China;2. Department of Mathematics, Shanghai University, Shanghai, China |
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Abstract: | This article proposes a structure-preserving quaternion full orthogonalization method (QFOM) for solving quaternion linear systems arising from color image restoration. The method is based on the quaternion Arnoldi procedure preserving the quaternion Hessenberg form. Combining with the preconditioning techniques, we further derive a variant of the QFOM for solving the linear systems, which can greatly improve the rate of convergence of QFOM. Numerical experiments on randomly generated data and color image restoration problems illustrate the effectiveness of the proposed algorithms in comparison with some existing methods. |
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Keywords: | color image restoration preconditioning techniques quaternion Arnoldi procedure quaternion full orthogonalization method |
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