A comparison of error estimates at a point and on a set when solving ill-posed problems
Abstract
The problem of correlating the error estimates at a point and on a correctness class is of interest to many mathematicians. Since the desired solution to a real ill-posed problem is unique, the error estimate obtained on the class becomes crude. In this paper, by assuming that an exact solution is a piecewise smooth function, we prove, for a special class of incorrect problems, that an error estimate at a point is an infinitely small quantity compared with an exact estimate on a correctness set.
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Articles in the same Issue
- Frontmatter
- Teacher, mentor, and friend. In honor of the 80th birthday of Professor Anatoly Borisovich Bakushinsky
- Source conditions and accuracy estimates in Tikhonov’s scheme of solving ill-posed nonconvex optimization problems
- Fast numerical method of solving 3D coefficient inverse problem for wave equation with integral data
- Solution of the inverse elastography problem for parametric classes of inclusions with a posteriori error estimate
- Imaging of buried objects from multi-frequency experimental data using a globally convergent inversion method
- Inverse source problem for parabolic equation with the condition of integral observation in time
- A comparison of error estimates at a point and on a set when solving ill-posed problems
- On TSVD regularization for a Broyden-type algorithm
Articles in the same Issue
- Frontmatter
- Teacher, mentor, and friend. In honor of the 80th birthday of Professor Anatoly Borisovich Bakushinsky
- Source conditions and accuracy estimates in Tikhonov’s scheme of solving ill-posed nonconvex optimization problems
- Fast numerical method of solving 3D coefficient inverse problem for wave equation with integral data
- Solution of the inverse elastography problem for parametric classes of inclusions with a posteriori error estimate
- Imaging of buried objects from multi-frequency experimental data using a globally convergent inversion method
- Inverse source problem for parabolic equation with the condition of integral observation in time
- A comparison of error estimates at a point and on a set when solving ill-posed problems
- On TSVD regularization for a Broyden-type algorithm
