The inexact, inexact perturbed, and quasi-Newton methods are equivalent models
The inexact, inexact perturbed, and quasi-Newton methods are equivalent models
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不精确、不精确摄动和拟牛顿方法是等效模型
DOI：
10.1090/s0025-5718-04-01646-1
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
E. Catinas
中科院分区：
文献类型：
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作者：
E. Catinas
拟牛顿方法给出了考虑误差项的经典牛顿迭代模型，该模型在每一步都假定扰动雅可比矩阵。它的高收敛阶由Dennis和More[数学]描述。[p. 28(1974), 549-560]。不精确牛顿法构成了另一种这样的模型，因为它假设在每一步线性系统只是近似解；这些迭代的高收敛阶由Dembo， Eisenstat和Steihaug [SIAM J. number]表征。植物学报，19(1982),400-408]。我们最近考虑了不精确摄动牛顿法[J]。Optim。理论应用，108(2001)，543 570]它假设在每一步线性系统都是摄动的，然后它们只是近似解；我们从扰动和残差的角度刻画了这些迭代的高收敛阶。在本文中，我们证明这三个模型实际上是等价的，因为每个模型都可以用来表征其他两个模型的高收敛阶。我们还研究了线性收敛情况下的关系，并推导出一个新的收敛结果。
A classical model of Newton iterations which takes into account some error terms is given by the quasi-Newton method, which assumes perturbed Jacobians at each step. Its high convergence orders were characterized by Dennis and More [Math. Comp. 28 (1974), 549-560]. The inexact Newton method constitutes another such model, since it assumes that at each step the linear systems are only approximately solved; the high convergence orders of these iterations were characterized by Dembo, Eisenstat and Steihaug [SIAM J. Numer. Anal. 19 (1982), 400-408]. We have recently considered the inexact perturbed Newton method [J. Optim. Theory Appl. 108 (2001), 543 570] which assumes that at each step the linear systems are perturbed and then they are only approximately solved; we have characterized the high convergence orders of these iterates in terms of the perturbations and residuals. In the present paper we show that these three models are in fact equivalent, in the sense that each one may be used to characterize the high convergence orders of the other two. We also study the relationship in the case of linear convergence and we deduce a new convergence result.
日本儿童和学生对 TIMSS 科学论文式任务的反应特征 (7) - 9 项任务分析结果的趋势 -
DOI：
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发表时间：
2005
期刊：
日本科学教育学会年会論文集 第29号
影响因子：
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作者：
中山 迅;大場裕子;猿田祐嗣
通讯作者：
猿田祐嗣