Spectral Analysis of an Inverse Problem

  • Francisco Duarte Moura Neto
  • Antônio José da Silva Neto


In this chapter we treat the solution of systems of linear equations in finite dimension spaces. This can be seen as examples of inverse reconstruction problems of Type I.We present a mathematical analysis of these linear inverse problems of finite dimension based on the spectral theorem.We study several aspects and behaviour of well-established methods for solving inverse problems. In particular, the concept of regularization, a very important notion in the area of inverse problems, will be dealt with. The analysis presented here is elementary – it depends on notions of linear algebra and convergence of numerical series. A similar study of regularization for problems in infinite dimensional spaces depends on functional analysis and is beyond the scope of this book. The interested reader is encouraged to consult [44, 29].


Inverse Problem Conjugate Gradient Search Direction Regularization Parameter Steep Descent 
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Copyright information

© Springer Berlin Heidelberg 2013

Authors and Affiliations

  • Francisco Duarte Moura Neto
    • 1
  • Antônio José da Silva Neto
    • 2
  1. 1.Instituto PolitécnicoUniversidade do Estado do Rio de JaneiroNova FriburgoBrazil
  2. 2.Departamento de Engenharia MecânicaUniversidade do Estado do Rio de JaneiroNova FriburgoBrazil

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