Exercise 3: Program for Tikhonov's methods.

Now write a program that solves equation (9) using the same matrix A as in the previous problem. Try several different values for the regularization parameter and compare these solutions with those you obtained using the singular value decomposition method. You might notice the similarity of equation (9) with the least squares solution (). Try setting and see what happens (explain).

To investigate the regularization of ill-posed problems further, see [16,17,18,19]. A particularly useful reference for discrete ill-posed problems is the Matlab package developed by Per Christian Hansen which is available via netlib [20].