Numerical comparison between Tikhonov regularization and singular value decomposition methods using the L curve criterion

Many problems in chemistry, physics and engineering requires the inversion of a Fredholm integral equation of first order. To find the solution of thi s problem one has to deal with ill-posed problem and special techniques hav e to be used. In this. paper two of the most common methods, the Tikhonov r egularization and the singular value decomposition, are compared when findi ng the solution of a model integral equation. The regularization parameter in the Tikhonov regularization and the dimension of the subspaces in the si ngular value decomposition were chosen using the L curve criterion. The ana lytical solution of the model integral equation was taken as a reference to analyze the results. The advantages of each method, with the presence of e rrors in the data, is presented and it is argumented the superiority of the singular value decomposition when dealing with this kind of problem.