Smoothed projection methods for the moment problem. (English) Zbl 0722.65096
The problem of reconstructing an unknown function f from a finite set of moments is discussed. The proposed algorithm is based on a point-wise optimization of the point-spread function. The method has several advantages: The ill-posed part of the reconstruction is contained in the construction of the basis functions. This step is independent of the data and can be done in advance with any desired accuracy. Then the algorithm proceeds by a point-wise reconstruction of the function f which is fast and makes the method suitable for local reconstructions.
The authors prove the convergence and the rate of convergence of their method and compare it with known methods as Backus-Gilbert and projection methods. The influence of noisy data is discussed and some numerical examples are given.
The authors prove the convergence and the rate of convergence of their method and compare it with known methods as Backus-Gilbert and projection methods. The influence of noisy data is discussed and some numerical examples are given.
Reviewer: G.Grozev (Sofia)
MSC:
| 65R20 | Numerical methods for integral equations |
| 65R10 | Numerical methods for integral transforms |
| 65R30 | Numerical methods for ill-posed problems for integral equations |
| 44A60 | Moment problems |
| 45B05 | Fredholm integral equations |
Keywords:
smoothed projection methods; integral equations of first kind; moment problem; ill-posed problems; algorithm; reconstruction; rate of convergence; noisy data; numerical examplesReferences:
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