WIAS Preprint No. 109, (1994)

On the stabilization of trigonometric collocation methods for a class of ill-posed first kind equations


  • Bruckner, Gottfried

2010 Mathematics Subject Classification

  • 65R30


  • Regularization-discretization procedures, moderately ill-posed, boundary integral equations, convergence rates




In this paper regularization-discretization procedures are developed for the numerical solution of moderately ill-posed linear first kind equations appearing as boundary integral equations for Dirichlet boundary value problems, e.g. the Dirichlet-Laplace problem. The method consists in firstly regularizing the noisy right-hand side by trigonometric interpolation and then applying a trigonometric collocation procedure to the regularized data. Convergence rates are obtained in Sobolev spaces, Hölder-Zygmund spaces or Hölder spaces according to the error analysis of the used procedures for exact data. The method can be generalized to other kinds of equations and approximation procedures.

Appeared in

  • J Inverse Ill-posed Problems 5 (1997), pp. 117-127.

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