α-β广义逆的迭代法

Iterative Methods for α-β Generalized Inverses

广义逆的性质在数值分析与数理统计等领域中有着非常重要的作用,而迭代方法在求解广义逆的实际问题中是一种非常有效的方法.本文主要利用矩阵α-β广义逆的相关性质,给出了α-β广义逆的四种迭代格式,并研究每种迭代格式收敛的充分必要条件.同时利用Frobenius范数给出了迭代收敛的误差界.最后给出数值算例,表明本文所提出的迭代格式对于计算α-β广义逆是非常有效的.

The properties of the generalized inverse play a very important role in numerical analysis and mathematical statistics, and the iterative method is a very effective method in solving practical problems of the generalized inverse. In this paper, we give four types of iterative schemes of the α-β generalized inverse through using the properties of the α-β generalized inverse of matrices. We further investigate the necessary and sufficient conditions for the convergence of each iterative method for the α-β generalized inverse. Besides, we give the error bounds of the iterative convergent procedures by Frobenius Norm. Finally, we depict one numerical example, which shows that the proposed iterative schemes are very effective in computing the α-β generalized inverse.