Solution of Ill-Posed Volterra Equations via Variable-Smoothing Tikhonov Regularization

Patricia K. Lamm
Department of Mathematics
Michigan State University
E. Lansing, MI 48824-1027

In: Inverse Problems in Geophysical Applications, edited by H. W. Engl, A. K. Louis, and W. Rundell, SIAM, 1997, pp 92-108.



Abstract:

We consider a ``local'' Tikhonov regularization method for ill-posed Volterra problems. In addition to leading to efficient numerical schemes for inverse problems of this type, a feature of the method is that one may impose varying amounts of local smoothness on the solution, i.e., more regularization may be applied in some regions of the solution's domain, and less in others. Here we present proofs of convergence for the infinite-dimensional local regularization problem and discuss the resulting numerical algorithm.


Text of paper:


Contact: lamm@math.msu.edu