Discretization and regularization are required steps to provide a stable approximation when solving integral equations of the first kind. The integral operator involved may be approximated by a sequence of finite rank operators and then the regularization procedure is applied. On the other hand, a regularization procedure can be conceived prior to the discretization. Both approaches are developed, implemented and compared for certain projection based methods.

中文翻译：

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离散化和正则化顺序对解决不适定问题的影响

在求解第一类积分方程时，离散化和正则化是提供稳定近似所需的步骤。所涉及的积分算子可以通过一系列有限秩算子来近似，然后应用正则化过程。另一方面，可以在离散化之前设想正则化过程。这两种方法都是针对某些基于投影的方法而开发、实施和比较的。