The pre/post equilibrated conditioning methods to solve Cauchy problems

Chein-Shan Liu

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The pre/post equilibrated conditioning methods to solve Cauchy problems

机译：解决柯西问题的前后平衡调理方法

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摘要

In the present paper, the inverse Cauchy problems of Laplace equation and biharmonic equation are transformed, by using the method of fundamental solutions (MFS) and the Trefftz method (TM), to the systems of linear equations for determining the expansion coefficients. Then, we propose three different conditioners together with the conjugate gradient method (CGM) to solve the resultant ill-posed linear systems. They are the post-conditioning CGM and the pre-conditioning CGM based on the idea of equilibrated norm for the conditioned matrices, as well as a minimum-distance conditioner. These algorithms are convergent fast and accurate by solving the inverse Cauchy problems under random noise.

机译：本文采用基本解法（MFS）和特雷夫兹法（TM），将拉普拉斯方程和双调和方程的柯西逆问题转化为线性方程组，以确定膨胀系数。然后，我们提出了三种不同的调节器以及共轭梯度法（CGM）来解决由此产生的不适定线性系统。它们是基于条件矩阵均衡范式思想的后条件CGM和条件CGM，以及最小距离条件器。通过解决随机噪声下的柯西逆问题，这些算法可以快速，准确地收敛。

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来源
《Engineering analysis with boundary elements》 |2014年第3期|62-70|共9页
作者
Chein-Shan Liu;
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作者单位

Department of Civil Engineering, National Taiwan University, Taipei, Taiwan;

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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
关键词
Inverse Cauchy problem; Laplace equation; Biharmonic equation; Equilibrated conditioning; Method of fundamental solutions; Trefftz method; Pre/post conjugate gradient method;

机译：柯西逆问题;拉普拉斯方程双谐方程平衡条件;基本解决方法;Trefftz方法;前后共轭梯度法;

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KKT is a science wing that tries to solve human problems with a wider perspective aimed at solving problematic human behaviors (Plumb, Stewart, Dahl and Lundgren, 2009). It is seen that there is very little research about the new approach of ACT approach when the aiming country of our country is screened and it is thought that our country will contribute to the field of psychological counseling with the work done. In the scope of the research, experimental and control groups and preliminary test, post-test and follow-up measurements of 2x3 experimental design were used. The study's study group consists of a total of 24 (12 experimental and 12 control groups) university students studying in different departments and levels, continuing their education in the academic year of 2015-2016 in Ağrı province and İbrahim Chechen University in 2015-2016 academic year. The average age of participants in the experiment and control group is 20. There were 12 participants in the experimental group, 7 female and 5 male, and 12 participants, 7 female and 5 male in the control group. Personal Information Form and Decision Making Style Scale prepared by the researcher were used in the research. In order to decide on the tests to be used in the course of analyzing the data, the scores of the participant's Decision Styles Scale pre-test, which are placed primarily in the experimental and control groups, it was analyzed whether the basic expectations of parametric tests were answered. As a result of the analysis made, the scores, skewness and kurtosis coefficients obtained from the Decision Making Styles Scale were given to the experimental and control groups. It was determined that the distribution was normal in the result of Shapiro-Wilk test, in which the skewness and kurtosis coefficients of each sub-scale were ranked between -1 and +1. 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The pre/post equilibrated conditioning methods to solve Cauchy problems

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