杨素华,欧阳兆福,罗兴钧,彭玉兵.求解Lavrentiev迭代方程的多尺度快速配置算法[J].数学年刊A辑,2017,38(4):419~432
求解Lavrentiev迭代方程的多尺度快速配置算法
Fast Multiscale Collocation Methods for Solving Iterated Lavrentiev Equations
Received: July 23, 2015  Revised: September 26, 2016
DOI:10.16205/j.cnki.cama.2017.0034
中文关键词:  Fredholm integral equation of the first kind, Iterated Lavrentiev regularization, Multiscale collocation method, A posteriori parameter choice strategy
英文关键词:Fredholm integral equation of the first kind, Iterated Lavrentiev regularization, Multiscale collocation method, A posteriori parameter choice strategy
基金项目:本文受到国家自然科学基金(No.11361005,No.11761010,No.61502107),江西省自然科学基金 (No.20151BAB201011)和江西省研究生创新基金(No.YC2015-S376)的资助.
Author NameAffiliationE-mail
YANG Suhua School of Mathematics and Computer Science, Gannan Normal University,Ganzhou 341000, Jiangxi, China. 1044791362@qq.com 
OUYANG Zhaofu School of Mathematics and Computer Science, Gannan Normal University,Ganzhou 341000, Jiangxi, China. ouyangzhaofu@foxmail.com 
LUO Xingjun School of Mathematics and Computer Science, Gannan Normal University,Ganzhou 341000, Jiangxi, China. lxj0298@126.com 
PENG Yubing School of Mathematics and Computer Science, Gannan Normal University,Ganzhou 341000, Jiangxi, China. pybmaths@163.com 
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中文摘要:
      考虑了第一类Fredholm积分方程的求解. 采用有矩阵压缩策略的多尺度配置方法来离散Lavrentiev迭代方程, 在积分算子是弱扇形紧算子时, 给出近似解的先验误差估计, 并给出了改进的后验参数的选择方法, 得到了近似解的收敛率. 最后, 举例说明算法的有效性.
英文摘要:
      The authors consider ill-posed Fredholm integral equations of the first kind. The authors apply a multiscale collocation method with a matrix compression strategy to discretize the iterated Lavrentiev equation and then analyze the priori convergence of the multiscale collocation method, if the integral operator is the weakly sectorial operator. The convergence rates of the iterated Lavrentiev regularization are achieved by using a modified a posteriori parameter choice strategy. Finally, numerical examples are given to illustrate the efficiency of the method.
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