Numerical regularization of a real inversion formula based on the Laplace transform's eigenfunction expansion of the inverse function

Abstract

We describe the numerical approximation of the inverse Laplace function based on the Laplace transform's eigenfunction expansion of the inverse function, in a real case. The error analysis allows us to introduce a regularization technique involving computable upper bounds of amplification factors of local errors introduced by the computational process. A regularized solution is defined as one which is obtained within the maximum attainable accuracy. Moreover the regularization parameter, that in this case coincides with the truncation parameter of the eigenfunction expansion, is dynamically computed by the algorithm itself in such a way that it provides the minimum of the global error bound.