Computable error estimators for the approximation of nonlinear problems by linearized models

Alexandra L. Chaillou; Manil Suri

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Computable error estimators for the approximation of nonlinear problems by linearized models

机译：通过线性化模型逼近非线性问题的可计算误差估计器

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摘要

In the modeling of nonlinear phenomena, a nonlinear model may often be replaced by a linear one, giving rise to a modeling or linearization error. This is in addition to the discretization error introduced when this linear model is solved, using, e.g., the finite element method. We investigate the a posteriori estimation of these errors for a general class of problems characterized by strongly monotone operators. Our results lead to the construction of computable upper estimators for the total error, with identifiable components from each of the these error sources. Several numerical tests evaluating the efficiency of our estimators are provided.

机译：在非线性现象的建模中，非线性模型通常可以由线性模型代替，从而引起建模或线性化误差。这是在使用例如有限元法求解线性模型时引入的离散误差的补充。对于以强单调算子为特征的一般问题，我们研究了这些错误的后验估计。我们的结果导致针对总误差构建了可计算的上估计量，并从这些误差源中的每一个中识别出分量。提供了一些评估我们的估计器效率的数值测试。

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《Computer Methods in Applied Mechanics and Engineering》 |2006年第3期|p.210-224|共15页
作者
Alexandra L. Chaillou; Manil Suri;
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作者单位

Department of Mathematics, College of Notre Dame, Baltimore, MD 21210, USA;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类自动化基础理论;工程基础科学;
关键词
A posteriori; estimator; linearization; nonlinear elasticity;

机译：后验估计量线性化非线性弹性;

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1. ASYMPTOTIC DISTRIBUTIONS OF SOME SCALE ESTIMATORS IN NONLINEAR MODELS WITH LONG MEMORY ERRORS HAVING INFINITE VARIANCE [J] . Koul Hira L., Surgailis Donatas Journal of Time Series Analysis . 2018,第3期

机译：具有无限方差的具有大内存误差的非线性模型中某些尺度估计的渐近分布
2. On Hong-Tamer's estimator in nonlinear errors-in-variable regression models [J] . Wu Jianghong, Song Weixing Statistics & Probability Letters . 2015,第Null期

机译：非线性变量误差回归模型中的Hong-Tamer估计
3. AN OPTIMAL JOINT ESTIMATOR FORREGRESSION PARAMETERS AND THE DISPERSION PARAMETERIN ERRORS-IN-VARIABLES NONLINEAR MODELS [J] . A. L. MALENKO, O. G. KUKUSH Theory of probability and mathematical statistics . 2008,第Null期

机译：回归参数和色散参数变量非线性模型的最优联合估计
4. Indirect Adaptive Fuzzy Control with Approximation Error Estimator for Nonlinear Systems [C] . Yongping Pan, Daoping Huang, Zonghai Sun 2009 Second international conference on intelligent computation technology and automation . 2009

机译：非线性系统的近似误差估计间接自适应模糊控制。
5. ESTIMATORS FOR THE NONLINEAR ERRORS-IN-VARIABLES MODEL. [D] . SCHNELL, DANIEL J. 1987

机译：非线性误差模型的估计器。
6. Simultaneous Bayesian Inference for Linear Nonlinear and Semiparametric Mixed-Effects Models with Skew-Normality and Measurement Errors in Covariates [O] . Yangxin Huang, Ren Chen, Getachew Dagne -1

机译：具有偏正态和测量误差的线性非线性和半参数混合效应模型的同时贝叶斯推断
7. Asymptotic properties of an estimator in nonlinear functional errors-in-variables models with dependent error terms [O] . Fazekas I., Kukush A.G. 1997

机译：具有相关误差项的非线性泛函误差模型中估计量的渐近性质
8. Recursive Prediction Error Parameter Estimator for Nonlinear Models [R] . Chen, S., Billings, S. A. 1987

机译：非线性模型的递推预测误差参数估计

Computable error estimators for the approximation of nonlinear problems by linearized models

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