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Numerical investigation of Fredholm integral equation of the first kind with noisy data
Mathematical Sciences ( IF 1.9 ) Pub Date : 2019-08-29 , DOI: 10.1007/s40096-019-00296-7
Hamid Mesgarani , Yaqub Azari

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:

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。
更新日期:2019-08-29
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