Regularization by projection: Approximation theoretic aspects and distance functions
Regularization by projection: Approximation theoretic aspects and distance functions
复制标题
通过投影正则化：近似理论方面和距离函数
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
S. Pereverzev
中科院分区：
文献类型：
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作者：
B. Hofmann;P. Mathé;S. Pereverzev
摘要 作者利用投影方法研究了非线性反问题的正则化。非线性由某些范围不变性假设控制。重点是决定收敛速度的离散化的近似理论特性。作者没有使用真实解的源条件来表示误差，而是展示了相对于某些基准平滑度的距离函数如何能够替代它。一些例子表明了如何应用结果。
Abstract The authors study regularization of non-linear inverse problems by projection methods. Non-linearity is controlled by some range invariance assumption. Emphasis is on approximation theoretic properties of the discretization which determine the convergence rates. Instead of using source conditions for the true solution to represent the error, the authors show how distance functions with respect to some benchmark smoothness are able to replace this. Some examples indicate how the results can be applied.