On a spectral approach to the construction of local regularization algorithms. (English. Russian original) Zbl 0691.47013
Sov. Math., Dokl. 39, No. 1, 86-90 (1989); translation from Dokl. Akad. Nauk SSSR 304, No. 3, 521-525 (1989).
The authors introduce a “local” regularization method for ill-posed linear operator equations in Hilbert space. The method depends on the so- called spectral resolution function of elements of the space and a known function which is a “spectral majorant of the error”. The ideas are illustrated for an iterative local regularization method and continuous local regularization methods for convolution equations.
Reviewer: Ch.W.Groetsch
MSC:
| 47A50 | Equations and inequalities involving linear operators, with vector unknowns |
| 65J10 | Numerical solutions to equations with linear operators |
| 49M99 | Numerical methods in optimal control |
