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A Survey of Regularization Methods for First-Kind Volterra Equations

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Surveys on Solution Methods for Inverse Problems

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.

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Authors and Affiliations

  1. Mathematics Dept., Michigan State University, E. Lansing, MI, 48824-1027, USA

    Patricia K. Lamm

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  1. Patricia K. Lamm
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Editors and Affiliations

  1. Department of Mathematical Sciences, University of Delaware, Newark, Delaware, USA

    David Colton

  2. Institut für Mathematik, Johannes-Kepler-Universität, Linz, Austria

    Heinz W. Engl

  3. Fachbereich Mathematik, Universität des Saarlandes, Saarbrücken, Federal Republic of Germany

    Alfred K. Louis

  4. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York, USA

    Joyce R. McLaughlin

  5. Department of Mathematics, Texas A & M University, College Station, Texas, USA

    William Rundell

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© 2000 Springer-Verlag/Wien

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Lamm, P.K. (2000). A Survey of Regularization Methods for First-Kind Volterra Equations. In: Colton, D., Engl, H.W., Louis, A.K., McLaughlin, J.R., Rundell, W. (eds) Surveys on Solution Methods for Inverse Problems. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6296-5_4

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  • DOI: https://doi.org/10.1007/978-3-7091-6296-5_4

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83470-1

  • Online ISBN: 978-3-7091-6296-5

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