| Fredholm积分方程的正则化GMRES算法 |
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| 引用本文： | 闵涛,赵苗苗,谷明礼.Fredholm积分方程的正则化GMRES算法[J].计算机工程,2012,38(4):239-240. |
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| 作者姓名： | 闵涛 赵苗苗 谷明礼 |
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| 作者单位： | 西安理工大学理学院,西安,710054 |
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| 基金项目： | 国家自然科学基金资助项目（50979088） |
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| 摘 要： | 利用数值求积公式，对二维第1类Fredholm积分方程进行离散处理，引入正则化GMRES算法，将离散后的积分方程转化为离散适定问题，通过广义极小残余算法得到其数值解。数值模拟结果表明，正则化GMRES算法求解二维第1类Fredholm积分方程计算速度快、精度高。
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| 关 键 词： | 数值求积 正则化法 Fredholm积分方程 适定问题 GMRES算法 |
| 收稿时间： | 2011-07-13 |
Regularization GMRES Algorithm for Fredholm Integral Equation |
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| MIN Tao
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ZHAO Miao-miao
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GU Ming-li.Regularization GMRES Algorithm for Fredholm Integral Equation[J].Computer Engineering,2012,38(4):239-240. |
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| Authors: | MIN Tao ZHAO Miao-miao GU Ming-li |
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| Affiliation: | (School of Sciences, Xi＇an University of Technology, Xi＇an 710054, China) |
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| Abstract: | Using numerical integration formula, the two-dimensional Fredholm integral equation is discrete. By introducing the regularization method, the discredited integral equation is transformed into a posed problem of discrete and the numerical solution is obtained by Generalized Minimal Residual（GMRES） algorithm. In the numerical simulation, different methods are compared with regularization GMRES method. The results show that the regularization GMRES method have advantages for solving two-dimensional first kind Fredholm integral equation with high computing speed and high accuracy. |
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| Keywords: | numerical integration regularization method Fredholm integral equation posed problem Generalized Minimal Residual（GMRES） algorithm |
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