| 一个新的连分式算法及其收敛性 |
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| 引用本文： | 陈开周,王孔明.一个新的连分式算法及其收敛性[J].计算数学,1988,10(1):35-43. |
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| 作者姓名： | 陈开周 王孔明 |
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| 作者单位： | 西北电讯工程学院应用数学系
(陈开周)，西北电讯工程学院应用数学系(王孔明) |
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| 摘 要： | 本文利用连分式插值,得到了一个新的一维搜索方法——连分式算法.用此算法,每迭代一次,只需计算三个点的函数值;在计算连分式插值式的每个系数时,只需一次除法.因此,数值稳定性较好.本文还证明了此算法的收敛性,收敛速度较快,收敛阶近似1.8393.按效能指标E=P~(1/μ)评价,此算法是一个较好的局部一维搜索方法.如果用此法于不精确的一维搜索,因只需计算三个点的函数值,故它是一个较好的、不精确的一维搜索方法,同时也是解超越方程的一个新算法.数值例子表明,它确实有效.
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A NEW CONTINUED FRACTION ALGORITHM AND ITS CONVERGENCE |
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| Institution: | Chen Kai-zhou;Wang Kong-ming Northwest Telecommunication Engineering Institute |
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| Abstract: | This paper proposes a new linear search method: the continued fraction algorithm. It re-quires computing only three functional values at each iteration, and using one division in com-puting every coefficient of the continued fraction interpolation. Its numerical stability is good,and its convergence rate is fast. The order of convergence is approximately 1.8393. Thus, thisalgorithm is a very attractive method for the local one-dimensional optimization. If we usethis method for the imprecise linear search, it is necessary only to compute three functional va-lues. It can also be applied to solve the transcendental equation. |
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