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A regularization framework for mildly ill-posed problems connected with pseudo-differential operator. (English) Zbl 1440.65281

The authors present a filter-based regularization method for mildly ill-posed problems involving pseudo-differential operators, the general framework of which was formulated in the reviewer’s work [Numer. Math. 68, No. 4, 469–506 (1994; Zbl 0817.65041)] and in [Dihn Nho Hào and H. Sahli, Vietnam J. Math. 32, 143–152 (2004; Zbl 1082.47044)].
The authors prove some error estimates for a priori and a posteriori regularization parameter strategies which are of optimal order under the standard smoothness source conditions. Some numerical experiments are presented to demonstrate the efficiency of the method.

MSC:

65R30 Numerical methods for ill-posed problems for integral equations
65D25 Numerical differentiation
35R30 Inverse problems for PDEs
53C35 Differential geometry of symmetric spaces
65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
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