On steplength algorithms for a class of continuation methods siam j numer anal
On steplength algorithms for a class of continuation methods siam j numer anal
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DOI：
10.1137/0718066
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发表时间：
1981-10
期刊：
影响因子：
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通讯作者：
den C. Heijer;W. Rheinboldt
中科院分区：
文献类型：
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作者：
den C. Heijer;W. Rheinboldt
这里考虑的延拓方法是计算分析形式为$Fx = b，F:D \子集R^{n + 1} \到R^n $的方程解域的正则部分的算法，对于给定$b \在R^n $中。虽然这些方法在结构上与用于ode求解器的方法相似，但它们的误差与过程的历史无关，并且完全由当前步骤的校正器的终止准则决定。这建议使用校正器收敛半径的后验估计。本文证明了这种估计不能单独从校正器迭代序列中获得，而需要关于f的一些全局信息。然而，证明了有限校正器迭代序列确实允许计算某些类型校正器收敛质量的有效估计。这是用于设计各种步进算法的延续过程；其中两个是基于牛顿校正器，而第三个是基于牛顿校正器。
The continuation methods considered here are algorithms for the computational analysis of the regular parts of the solution field of equations of the form $Fx = b,F:D \subset R^{n + 1} \to R^n $, for given $b \in R^n $. While these methods are similar in structure to those used for ODE-solvers, their errors are independent of the history of the process and are solely determined by the termination criterion of the corrector at the current step. This suggests the use of a posteriors estimates of the convergence radii of the corrector. It is proved here that such estimates cannot be obtained from the sequence of corrector iterates alone but that they require some global information about F. However, it is shown that a finite sequence of corrector iterates does allow for the computation of effective estimates of the convergence quality of certain types of correctors. This is used for the design of various step-algorithms for continuation processes; two of them are based on a Newton-corrector while the third o...