A survey of regularization methods for first-kind Volterra equations
Patricia K. Lamm
Department of Mathematics
Michigan State University
E. Lansing, MI 48824-1027
Surveys on Solution Methods for Inverse
Problems
D. Colton, H. W. Engl, A. Louis,
J. R. McLaughlin, W. Rundell, Editors
Springer (Vienna, New
York), pp 53-82, 2000.
Abstract:
We survey continuous and discrete regularization methods for
first-kind Volterra problems with continuous kernels. Classical
regularization methods tend to destroy the non-anticipatory (or
causal) nature of the original Volterra problem because such methods
typically rely on computation of the Volterra adjoint operator, an
anticipatory operator. In this survey we pay special attention to
particular regularization methods, both classical and nontraditional,
which tend to retain the Volterra structure of the original
problem. Our attention will primarily be focused on linear problems,
although extensions of methods to nonlinear and integro-operator
Volterra equations are mentioned when known.
Text of paper:
Contact: lamm@math.msu.edu