Abstract
In order to understand the concentrating mechanism of the mammalian kidneys, it is necessary to study the relationship between the parameter vector h (permeabilities of water and solutes) and the corresponding vector of concentration profiles V. We consider the inverse problem: determine h from a given V. This problem is ill-posed. Therefore, the regularization methods must be used to circumvent the ill-conditioning. We show how the Levenberg-Tikhonov-Marquard method with the Sobolev norm can be used to handle the inverse problem.
Original language | English |
---|---|
Pages (from-to) | 77-81 |
Number of pages | 5 |
Journal | Applied Mathematics Letters |
Volume | 9 |
Issue number | 3 |
DOIs | |
State | Published - May 1996 |
Bibliographical note
Funding Information:by Korean Ministry of Education, BSRI-95-1430 and Ewha Women’s University, 1994-3. by NSF Grant DMS921664 and NIH Grant DK1759314. Author to whom all correspondence
Keywords
- Ill-conditioning
- Kidney models
- Numerical methods
- Regularization