| Levin变换应用于欧拉常数数列及连分式数列改进算法的加速收敛 |
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| 引用本文： | 姚清照,贺黎明. Levin变换应用于欧拉常数数列及连分式数列改进算法的加速收敛[J]. 大学数学, 2021, 37(1): 5-9. DOI: 10.3969/j.issn.1672-1454.2021.01.002 |
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| 作者姓名： | 姚清照 贺黎明 |
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| 作者单位： | 华东理工大学 理学院,上海 200237;华东理工大学 理学院,上海 200237 |
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| 摘 要： | 利用Lu等人通过连分式修正更快收敛的欧拉常数数列及其相关余项式,进一步采用Levin变换进行二次加速,特别是在克服舍入误差的情况下,就能更有效地计算出欧拉常数的高精度数值结果.
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| 关 键 词： | 加速收敛 通用Levin变换 连分式 欧拉常数 舍入误差 |
Application of the General Levin Transformation to a Modified Continued Fraction Sequence towards Euler's Constant for Improving the Rate of Convergence |
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| YAO Qing-zhao,HE Li-ming. Application of the General Levin Transformation to a Modified Continued Fraction Sequence towards Euler's Constant for Improving the Rate of Convergence[J]. College Mathematics, 2021, 37(1): 5-9. DOI: 10.3969/j.issn.1672-1454.2021.01.002 |
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| Authors: | YAO Qing-zhao HE Li-ming |
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| Affiliation: | (School of Science, East China University of Science and Technology, Shanghai 200237, China) |
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| Abstract: | Lu et al.have derived a continued fraction sequence which converges to the Euler’s constant faster than the original sequence.One can accelerate the modified sequence with the remainder estimate by using the general Levin transformation and accurate numerical results can be obtained more efficiently,especially when computer algebra system Maple is used to get rid of round-off errors. |
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| Keywords: | acceleration of convergence the general Levin transformation a continued fraction Euler’s constant round-off errors |
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