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中文摘要：
我们考虑解决线性提出病的操作员方程。基于多尺度的分解解决方案空格，我们为解决方程建议多参数规则化。我们为多参数规则化答案建立弱、强壮的集中定理。基于特徵函数分解，特别地，我们为与最佳的错误界限给一个规则化答案的多参数开发后验选择策略。多参数的几种实际选择被建议。我们也介绍数字实验示威外面在单个参数规则化上的经产妇米规则化的性能。
英文摘要：
We consider solving linear ill-posed operator equations. Based on a multi-scale decomposition for the solution space, we propose a multi-parameter regularization for solving the equations. We establish weak and strong convergence theorems for the multi-parameter regularization solution. In particular, based on the eigenfunction decomposition, we develop a posteriori choice strategy for multi-parameters which gives a regularization solution with the optimal error bound. Several practical choices of multi-parameters are proposed. We also present numerical experiments to demonstrate the outperformance of the multiparameter regularization over the single parameter regularization.
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