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 this problem one has to deal with ill-posed problem and special techniques have to be used. In this. paper two of the most common methods, the Tikhonov regularization and the singular value decomposition, are compared when finding the solution of a model integral equation. The regularization parameter in the Tikhonov regularization and the dimension of the subspaces in the singular value decomposition were chosen using the L curve criterion. The analytical solution of the model integral equation was taken as a reference to analyze the results. The advantages of each method, with the presence of errors in the data, is presented and it is argumented the superiority of the singular value decomposition when dealing with this kind of problem.