Numerical comparison between Tikhonov regularization and singular value decomposition methods using the L curve criterion (Q5950892)

To find the solution of the Fredholm integral equation of the first kind \[ \int_a^bK(x,y)f(y) dy=g(x), \] \(c\leqslant x\leqslant d,\) one has to deal with an 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 exact solution of a model integral equation. The regularization parameter in the Tikhonov regularization and the dimension of the subspaces in the singular value decomposition are chosen using the \(L\) curve criterion. The advantage of each method, with the presence of errors in the data, is presented and it is argumented that the singular value decomposition is superior when dealing with this kind of problem.