| 引用本文： |
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王华军,王硕,曹义超.求解线性逆问题的谱共轭梯度法[J].广西科学,2016,23(5):416-421,427. [点击复制]
- WANG Huajun,WANG Shuo,CAO Yichao.A Spectral Conjugate Gradient Method for Solving Linear Inverse Problems[J].Guangxi Sciences,2016,23(5):416-421,427. [点击复制]
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| 摘要: |
| 针对线性逆问题,把原问题的算子方程转化为带有Tikhonov正则项的无约束优化问题,提出一个求解线性逆问题的新谱共轭梯度法,并证明算法的全局收敛性.数值结果表明,新算法是有效的. |
| 关键词: 线性逆问题 谱共轭梯度法 Tikhonov正则项 |
| DOI：10.13656/j.cnki.gxkx.20161121.013 |
| 投稿时间：2016-03-15修订日期：2016-04-15 |
| 基金项目:国家自然科学基金项目(11361018),广西自然科学基金项目(2014GXNSFFA118001),广西高校中青年教师基础能力提升项目(ky2016YB167)和桂林电子科技大学研究生教育创新计划项目(2016YJCX46)资助。 |
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| A Spectral Conjugate Gradient Method for Solving Linear Inverse Problems |
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WANG Huajun, WANG Shuo, CAO Yichao
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| (School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin, Guangxi, 541004, China) |
| Abstract: |
| In this study,a new spectral conjugate gradient method is presented to solve linear inverse problems,which are transferred into the linear unconstrained optimization with Tikhonov regularization.The global convergence of the proposed scheme is analyzed.The new algorithm is compared with Landweber,TSVD and TV methods,and numerical results illustrate the efficiency of this method. |
| Key words: linear inverse problems spectral conjugate gradient method Tikhonov regularization |
