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Chapter 9: We report a large quantity of numerical experiments of 13 different algebraic multigrid algorithms for solving the Poisson equation, anisotropic equation, equation with cross-derivative terms, general matrix problems with large off-diagonal positive entries, biharmonic equation, Toeplity matrix, elasticity systems, finite element discretization of the Laplacian and even 3D problems. Particular attention is focused on asymptotic convergence factors and CPU-time consumed. Numerical results for many different types of practical problems demonstrate the efficiency and robustness of the proposed algebraic multigrid methods.

第九章:在各种代数多重网格算法的基础上,进行了大量的数值试验,具体给出了十三种不同的代数多重网格方法求解泊松方程,各向异性方程,带混合导数项的方程,带有大的非对角正元素的一般矩阵问题,重调和方程,托普利兹矩阵,弹性力学方程组,拉普拉斯算子的有限元离散,甚至三维问题的较为丰富的数值结果,重点关注它们的渐近收敛因子和所需的CPU时间,来源于不同类型问题的计算结果既为代数多重网格理论分析和算法的改进提供了很实用的资料,同时也证实了本文给出的代数多重网格算法的效绩和稳健性。

In the presently mobile position technology, GPS's position method is one of the best. This method owns high accuracy less than 15 meters, and can be used with GPS chip in the mobile station. But GPS chip with the high price makes this technology difficult to popular. Therefore, the position technology of GSM communication network is attention to the people gradually. TOA or AOA is more often used among position technology, these methods need only the help of the position measuring instrument to attain time and angle for position calculation. They have good position accuracy, but they are also too expensive to popular. Every positioning technology has its bottleneck such as external environment influence, cost and positing efficiency. Therefore, the purpose of this research lies in finding out the mobile station location and does not emphasize the raise of the accuracy and it only uses existing information to finish position action.

在目前的行动定位技术中,以GPS定位技术为最佳,不仅拥有少於15公尺的高定位精确度,更只需在行动端加装GPS晶片即可使用,可惜高价格的GPS晶片使得此技术难以普及化,因此,以GSM通讯网路为主的定位技术逐渐受人们所重视,其中,又以TOA或AOA等定位技术较常被使用,仅透过位置测量仪器的帮助,便可取得定位所需的时间和角度,并且拥有不错的定位精确度,可惜也受到高价格因素的关系难以普及化,而每种定位技术都有其瓶颈存在,不论是外在环境的影响、成本和定位效能上;所以,本研究的目的在於找出行动端位置,即利用现有的资讯(细胞识别码、讯号强度等)来完成定位动作,而非强调其定位精确度的提高。

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