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。
关键词:
数值求积,
正则化法,
Fredholm积分方程,
适定问题,
GMRES算法
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.
Key words:
numerical integration,
regularization method,
Fredholm integral equation,
posed problem,
Generalized Minimal Residual(GMRES) algorithm
中图分类号:
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(04): 239-240.
MIN Chao, DIAO Miao-Miao, GU Meng-Li. Regularization GMRES Algorithm for Fredholm Integral Equation[J]. Computer Engineering, 2012, 38(04): 239-240.