ON THE REGULARIZATION METHOD OF THE FIRST KIND OF FREDHOLM INTEGRAL EQUATION WITH A COMPLEX KERNEL AND ITS APPLICATION

Applied Mathematics and Mechanics (English Edition) ›› 1998, Vol. 19 ›› Issue (1): 75-83.

ON THE REGULARIZATION METHOD OF THE FIRST KIND OF FREDHOLM INTEGRAL EQUATION WITH A COMPLEX KERNEL AND ITS APPLICATION

尤云祥, 缪国平

Shanghai Jiaotong University, Shanghai 200030, P. R. China

收稿日期:1996-06-24 修回日期:1997-06-08 出版日期:1998-01-18 发布日期:1998-01-18

ON THE REGULARIZATION METHOD OF THE FIRST KIND OF FREDHOLM INTEGRAL EQUATION WITH A COMPLEX KERNEL AND ITS APPLICATION

You Yunxiang, Miao Guoping

Shanghai Jiaotong University, Shanghai 200030, P. R. China

Received:1996-06-24 Revised:1997-06-08 Online:1998-01-18 Published:1998-01-18

摘要/Abstract

摘要： The regularized intngrodifferential equation for the first kind of Fredholm integralequation with a complex kernel is derived by generalizing the Tikhonov regularizationmethod and the convergence of approximate regularized solutions is discussed. As anapplication of the method, an inverse problem in the two-demensional wave-makingproblem of a flat plate is solved numerically, and a practical approach of choosingoptimal regularization parameter is given.

关键词: inverse problem, Fredholm integral equation of the first kind, complex kernel, regularization method

Abstract: The regularized intngrodifferential equation for the first kind of Fredholm integralequation with a complex kernel is derived by generalizing the Tikhonov regularizationmethod and the convergence of approximate regularized solutions is discussed. As anapplication of the method, an inverse problem in the two-demensional wave-makingproblem of a flat plate is solved numerically, and a practical approach of choosingoptimal regularization parameter is given.

Key words: inverse problem, Fredholm integral equation of the first kind, complex kernel, regularization method

尤云祥;缪国平. ON THE REGULARIZATION METHOD OF THE FIRST KIND OF FREDHOLM INTEGRAL EQUATION WITH A COMPLEX KERNEL AND ITS APPLICATION[J]. Applied Mathematics and Mechanics (English Edition), 1998, 19(1): 75-83.

You Yunxiang;Miao Guoping . ON THE REGULARIZATION METHOD OF THE FIRST KIND OF FREDHOLM INTEGRAL EQUATION WITH A COMPLEX KERNEL AND ITS APPLICATION[J]. Applied Mathematics and Mechanics (English Edition), 1998, 19(1): 75-83.

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ON THE REGULARIZATION METHOD OF THE FIRST KIND OF FREDHOLM INTEGRAL EQUATION WITH A COMPLEX KERNEL AND ITS APPLICATION

ON THE REGULARIZATION METHOD OF THE FIRST KIND OF FREDHOLM INTEGRAL EQUATION WITH A COMPLEX KERNEL AND ITS APPLICATION

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