On the local regularization of inverse problems of Volterra type
Patricia K. Lamm
Department of Mathematics
Michigan State University
E. Lansing, MI 48824-1027
In Proc. 1995 ASME Design Engineering Technical
Conferences: Parameter Identification Symposium, September 1995,
Boston, MA.
Abstract:
We consider a local regularization method for the solution of first-kind
Volterra integral equations with convolution kernel. The local
regularization is based on a splitting of the original Volterra operator
into "local" and "global" parts, and a use of Tikhonov regularization
to stabilize the inversion of the local operator only. The
regularization parameters for the local procedure include the standard
Tikhonov parameter, as well as a parameter that represents the length of
the local regularization interval. We present a convergence theory for
the infinite-dimensional regularization problem and show that the
regularized solutions converge to the true solution as the
regularization parameters go to zero (in a prescribed way). In
addition, we show how numerical implementation of the ideas of local
regularization can lead to the notion of "sequential Tikhonov
regularization" for Volterra problems; this approach has been shown in
(Lamm and Elden, 1995) to be just as effective as Tikhonov regularization,
but to be much more efficient computationally.
Text of paper:
Contact: lamm@math.msu.edu