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Manuscript Title: A generalized regularization method for nonlinear ill-posed problems enhanced for nonlinear regularization terms.
Authors: T. Roths, M. Marth, J. Weese, J. Honerkamp
Program title: GENEREG
Catalogue identifier: ACGH_v3_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 139(2001)279
Programming language: Fortran.
Computer: Sun, Pentium PC.
Operating system: UNIX (SunOS), MS Windows, Linux.
RAM: 10M words
Word size: 32
Keywords: Ill-posed inverse problem, Regularization, Prior information, Tikhonov regularization, Edge preserving regularization, General purpose, Fit.
Classification: 4.9.

Nature of problem:
Many physically interesting functions are not directly accessible by experiments. However, they often can be inferred from an experimentally measurable quantity by solving an inverse problem. If the inverse problem is ill-posed, so-called regularization methods are necessary which impose prior information upon the solution. This prior information is modeled by the regularization term which may be nonlinear.

Solution method:
The nonlinear regularization method implemented in the program NLREG (for NonLinear REGularization) [1] is generalized for the ability to implement more general and in particular nonlinear regularization terms. This extended feature is discussed exemplarily by means of an edge preserving regularization method which makes use of a nonlinear regularization term [2].

Running time:
The typical running time is proportional to (n + ns)ns**2, in which n and ns denote the number of data points respectively the number of points at which the solution is calculated.

[1] J. Weese, Comput. Phys. Commun. 77 (1993) 429.
[2] T. Roths, D. Maier, Chr. Friedrich, M. Marth, J. Honerkamp, Rheol. Acta 39 (2000) 163.