Abstract: Influence of round-off error and truncation error on convergence property of iterative sequences is an important topic in scientific computing. Using functional theory, the rate of convergence for the contraction mapping iterative sequences with errors in metric space was analyzed. The optimal estimate for the order of convergence was obtained.

Key words: Iterative sequence with error, Metric space, Fixed-point, Order of convergence

摘要： 舍入误差和截断误差对迭代序列收敛性的影响是科学计算中的重要课题，利用泛函分析理论分析了完备度量空间中带有误差的压缩映射迭代序列的收敛速度，得到了迭代序列收敛阶的最佳估计。

关键词: 带有误差的迭代序列, 度量空间, 不动点, 收敛阶 