Maximum entropy regularization of Fredholm integral equations of the first kind
Maximum entropy regularization of Fredholm integral equations of the first kind
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DOI：
10.1088/0266-5611/7/6/004
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发表时间：
1991-12
期刊：
影响因子：
2.1
通讯作者：
U. Amato;W. Hughes
中科院分区：
文献类型：
--
作者：
U. Amato;W. Hughes
考虑了在已知f（x）>或=0时，用基于极小化的正则化方法数值求解第一类Fredholm积分方程的问题.这个最小化问题的解决方案的收敛性，给定的条件下的数据和正则化参数λ，证明了该过程导致一个正确的正则化方法。引入了一种广义交叉验证策略来选择正则化参数。进行了大量的数值实验，并与基于微分算子的Tikhonov正则化格式进行了比较。
The problem of solving numerically a Fredholm integral equation of the first kind when it is known that f(x)>or=0, by a regularization method based on minimization is considered. The convergence of solutions of this minimization problem, given conditions on the data and the regularization parameter lambda , is demonstrated to show that the procedure leads to a correct regularization method. A generalized cross validation strategy for the selection of the regularization parameter is introduced. A number of numerical experiments are made and comparisons are made with Tikhonov regularization schemes based on differential operators.