## 留言板

 引用本文: 尤云祥, 缪国平. 带复数核的第一类Fredholm积分方程的正则化方法及其应用*[J]. 应用数学和力学, 1998, 19(1): 70-78.
You Yunxiang, Miao Guoping. On the Regularization Method of the First Kind Fredholm Integral Equation With a Complex Kernel and its Application[J]. Applied Mathematics and Mechanics, 1998, 19(1): 70-78.
 Citation: You Yunxiang, Miao Guoping. On the Regularization Method of the First Kind Fredholm Integral Equation With a Complex Kernel and its Application[J]. Applied Mathematics and Mechanics, 1998, 19(1): 70-78.

## On the Regularization Method of the First Kind Fredholm Integral Equation With a Complex Kernel and its Application

• 摘要: 本文推广了Tikhonov正则化方法,导出了带复数核的第一类Fredholm积分方程的正则解应满足的正则积分微分方程,并讨论了正则解的收敛性.作为这一方法的应用,数值求解了与二维摇板造波问题相应的一类逆问题,并给出了选择最佳正则参数的一个实用的方法.
•  [1] J.Baumeister,Stable Solution of Inverse Problem,Vieweg & Ohn,Braunschweig/Wiesbaden(1987). [2] P.C.Sabatier(ed),Inverse Pr oblems :An In ter disciplinary Study,Academic Press Boston(1987). [3] A.N.Tikhonov and V.Y.Arsenin,Solution of Ill-posed Pr oblems,Wiley,New York(1977). [4] R.Kress,Linear Intergral Equations,Springer-Verlag,Berlin(1989). [5] A.N.Tikhonov,On solution of incorrectly formulated problems and the regularization method,Sovier Math.Doklady,4(1963),1035-1038.(English version) [6] D.L.Phillips,A technique for the numerical solution of certain intergral equations of the first kind,J.Ass.Comp.Math.,9(1962),84-97. [7] E.Schock,On the asymptotic order of accuracy of Tikhonov regularization,J.Optim.Theroy Appl.,44(1984),95-104. [8] 缪国平、刘应中编,《海洋工程水动力学基础》,海洋出版社,北京(1991). [9] 缪国平、刘应中,有限水深表面压力脉动产生的速度势与二阶绕射问题的辐射条件,中国造船,总107期(1989),1-13. [10] 李世雄、刘家绮编,《小波变换和反演数学基础》,地质出版社,北京(1994).
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##### 出版历程
• 收稿日期:  1996-06-24
• 修回日期:  1997-06-08
• 刊出日期:  1998-01-15

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