On the stabilization of trigonometric collocation methods for a class of ill-posed first kind equations
- Bruckner, Gottfried
2010 Mathematics Subject Classification
- 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.
- J Inverse Ill-posed Problems 5 (1997), pp. 117-127.