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Lavrentiev’s Method for Linear Volterra Integral Equations of the First Kind, with Applications to the Non-Destructive Testing of Optical-Fibre Preforms

  • Robert Plato

Abstract

In the non-destructive testing of optical-fibre preforms, the problem of determining the axial stress components from measurements of the phase retardation of laser lights sent through the object reduces to a generalized Abel integral equation of the first kind, for more details we refer to Section 4. The methods presented in this paper can be applied to solve those problems efficiently, and we begin more generally with the consideration of a linear Volterra integral equation of the first kind,
$$(Au)(t):=\int_{0}^{t} k(t,s)u(s) ds = f_{*} (t), t \in [0,a]$$
.

Keywords

Banach Space Discrepancy Principle Nondestructive Test Regularization Method Volterra Integral Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Wien 1997

Authors and Affiliations

  • Robert Plato
    • 1
  1. 1.Fachbereich MathematikTechnische Universität BerlinBerlinGermany

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