Jp. Braga, Numerical comparison between Tikhonov regularization and singular value decomposition methods using the L curve criterion, J MATH CHEM, 29(2), 2001, pp. 151-161
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.