We consider Fredholm integral equation of the first kind with noisy data and use Landweber-type iterative methods as an iterative solver. We compare regularization property of Tikhonov, truncated singular value decomposition and the iterative methods. Furthermore, we present a necessary and sufficient condition for the convergence analysis of the iterative method. The performance of the iterative method is shown and compared with modulus-based iterative methods for the constrained Tikhonov regularization.

中文翻译：

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含噪声数据的第一类Fredholm积分方程的数值研究。

我们考虑带有噪声数据的第一类Fredholm积分方程，并使用Landweber型迭代方法作为迭代求解器。我们比较了Tikhonov的正则化性质，截断的奇异值分解和迭代方法。此外，我们为迭代方法的收敛性分析提供了充要条件。显示了迭代方法的性能，并将其与基于约束的Tikhonov正则化的基于模量的迭代方法进行了比较。