| 无穷序列加速收敛的一个方法 |
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| 引用本文： | 单华宁. 无穷序列加速收敛的一个方法[J]. 南京理工大学学报(自然科学版), 1998, 22(6): 573-576 |
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| 作者姓名： | 单华宁 |
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| 作者单位： | 海军医学高等专科学校数理教研室!南京210099 |
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| 摘 要： | 该文通过研究无穷序列加速收敛方法，在Ｌｅｖｉｎ ｔ－变换的基础上，考虑了Ｌｅｖｉｎ ｔ－变换的迭代过程，提出了Ｌｅｖｉｎ ｔ－变换迭代法，指出了这种方法能加快序列的收敛速度，给出了理论证明，并且通过具体实例给予了证实。同时，此法形成了循环加速的过程，适合于在计算机上进行了计算，从而在实际应用中具有明显的优越性。对于交错级数部分和序列的加速收敛，所术方法较为有效。
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| 关 键 词： | 收敛 无穷离列 加速收敛 交错级数 部分和 |
A Method of Accelerating Convergence for Infinite Sequence |
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| Shan Huaning. A Method of Accelerating Convergence for Infinite Sequence[J]. Journal of Nanjing University of Science and Technology(Nature Science), 1998, 22(6): 573-576 |
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| Authors: | Shan Huaning |
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| Abstract: | In this paper,with the method of accelerating convergence of infinite sequence,based on L evin t- transform and its iterative process,the iteration method of L evin- ttransform is presented.Itis pointed out that this method can increase the rate of convergence of sequence,and it is confirmed by the specific examples.At the same time, this method forms a procedure ofsuccessive acceleration,and itis applicable forcomputing in computer.The method offers obvious advantages in practical use,especially in accelerating convergence of alterating series sequences. |
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| Keywords: | infinite sequences acceleration convergence |
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