未知噪声下获得最优收敛速度的修正偏差原理
A modified discrepancy principle to attain optimal convergence rates under unknown noise
摘要：
在希尔伯特空间中考虑一个线性不适定方程。右手侧的多个独立无偏测量是可用的。一种自然的方法是将测量值的平均值作为右手边的近似值，并将数据误差估计为测量值数量的平方根的倒数。我们计算的最佳收敛速度（作为测量的数量趋于无穷大）在经典的源条件下，并介绍了一个修改的差异原则，渐近达到这个速度。
英文摘要：
We consider a linear ill-posed equation in the Hilbert space setting. Multiple independent unbiased measurements of the right hand side are available. A natural approach is to take the average of the measurements as an approximation of the right hand side and to estimate the data error as the inverse of the square root of the number of measurements. We calculate the optimal convergence rate (as the number of measurements tends to infinity) under classical source conditions and introduce a modified discrepancy principle, which asymptotically attains this rate.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
