Cross-validation for parameter estimation in the BEM

摘要

We consider the application of the statistical technique of cross-validation to estimating parameters in a number of problems of importance in the BEM. They are: the estimation of the shape parameter for multiquadric approximation and the regularization parameter in the numerical approximation of the solution of ill-posed integral equations. The latter technique is illustrated by its use in the numerical inversion of the Laplace transform, a problem that occurs frequently in the numerical solution of time dependent partial differential equations. A variety of numerical results are presented illustrating the technique.