A mollification regularization method for stable analytic continuation. (English) Zbl 1218.30004
Summary: We consider an analytic continuation problem on a strip domain with data given approximately only on the real axis. The Gauss mollification method is proposed to solve this problem. An a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, we also propose a new a posteriori parameter choice rule and get a good error estimate. Several numerical examples are provided, which show that the method works effectively.
MSC:
| 30B40 | Analytic continuation of functions of one complex variable |
| 65J20 | Numerical solutions of ill-posed problems in abstract spaces; regularization |
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