带复数核的第一类Fredholm积分方程的正则化方法及其应用*
On the Regularization Method of the First Kind Fredholm Integral Equation With a Complex Kernel and its Application
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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.
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关键词:
- 逆问题 /
- 第一类Fredholm积分方程 /
- 复数核 /
- 正则化方法
Abstract: The regularized integrodifferential equation for the first kind Fredholm integral equation with a complex kernel is derived by generalizing the Tikhonov regularization method and the convergence of approximate rgeularized solutions is discussed. As an application of the method, an inverse problem in the two-demensional wave-making problem of a flat plate is solved numerically, and a practical approach of choosing optimal regularization parameter is given. -
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