科研之友
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摘要
Spectral enhancement-which aims to undospectral broadening-leads to integral equations which are ill-posed and require special regularization techniques for their solution. Even when an optimal regularization technique is used, however, the errors in the solution, which originate in data approximation errors, can be substantial and it is important to have good bounds on these errors in order to select appropriate enhancement methods. A discussion of the causes and nature of broadening provides regularity or source conditions which are required to obtain bounds for the regularized solution of the spectral enhancement problem. Only in special cases do the source conditions satisfy the requirements of the standard convergence theory for ill-posed problems. Instead we have to use variable Hilbert scales and their interpolation inequalities to get error bounds. The error bounds in this case turn out to be of the form O(epsilon(1-eta(epsilon))) where epsilon is the data error and eta(epsilon) is a function which tends to zero when epsilon, is the data error and eta(epsilon) is a function which tends to zero when epsilon trends to zero. The approach is demonstrated with the Eddington correction formula and applied to a new spectral reconstruction technique for Voigt spectra. In this case eta(epsilon) = O(1/root|log epsilon|) is found.
- 出版日期2010
