Regularization operators versus regularization strategies
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Thi-An Nguyen
Abstract
In this note, we shall compare two important concepts of “regularization operators” and “regularization strategies” that appear in different classical monographs. The definition of a regularization operator is related to the Moore–Penrose inverse of the operator. In general, a regularization operator is a regularization strategy. We shall show that the converse is also true under some conditions. It is interesting to note that these two systems share analogous properties.
Acknowledgements
We would like to thank National Science and Technology Council for partial support. We also thank the anonymous reviewers for their valuable comments.
References
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Uniqueness of the potential in a time-fractional diffusion equation
- A partial inverse problem for non-self-adjoint Sturm–Liouville operators with a constant delay
- Extracting discontinuity using the probe and enclosure methods
- A dynamical method for optimal control of the obstacle problem
- On the uniqueness of solutions in inverse problems for Burgers’ equation under a transverse diffusion
- On an inverse problem for a linearized system of Navier–Stokes equations with a final overdetermination condition
- Regularization operators versus regularization strategies
Artikel in diesem Heft
- Frontmatter
- Uniqueness of the potential in a time-fractional diffusion equation
- A partial inverse problem for non-self-adjoint Sturm–Liouville operators with a constant delay
- Extracting discontinuity using the probe and enclosure methods
- A dynamical method for optimal control of the obstacle problem
- On the uniqueness of solutions in inverse problems for Burgers’ equation under a transverse diffusion
- On an inverse problem for a linearized system of Navier–Stokes equations with a final overdetermination condition
- Regularization operators versus regularization strategies
