Effective Algorithms for Computing Global and Local Posterior Error Estimates of Solutions to Linear Ill-Posed Problems
| Autor: | Alexander S. Leonov |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Well-posed problem
General Mathematics 010102 general mathematics Hilbert space Maximization Inverse problem 01 natural sciences 010101 applied mathematics Constraint (information theory) symbols.namesake Quadratic equation symbols A priori and a posteriori Differentiable function 0101 mathematics Algorithm Mathematics |
| Zdroj: | Russian Mathematics. 64:26-34 |
| ISSN: | 1934-810X 1066-369X |
| Popis: | We consider extremal problems introduced and investigated earlier by the author for calculating global and local a posteriori error estimates of approximate solutions to ill-posed inverse problems. For linear inverse problems in Hilbert spaces, they consist in maximization of quadratic functionals with two quadratic constraints. The article shows how under certain conditions these problems can be reduced to a problem of maximization of a special (written analytically) differentiable functional with one constraint. New algorithms for calculating global and local a posteriori error estimates based on the solution of these problems are proposed. Their effectiveness is illustrated by numerical experiments on a posteriori error estimation of solutions to the model two-dimensional inverse problem of potential continuation. Experiments show that the proposed algorithms give a posteriori error estimates close to the true error values. Proposed algorithms for global a posteriori error estimation turn out to be more rapid (3 to 5 times) than the previously known algorithms. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink