As an example of the simplest of Tikhonov's methods, consider minimizing
the following functional for the solution vector **z**:

which yields:

This is the Tikhonov method with zeroth order regularization with
regularization parameter . The * zeroth order* corresponds to
the inclusion of the identity matrix in equation
(9).

Other matrices that are used in practice include numerical approximations of the gradient or Laplacian, depending on which characteristic of the solution one is trying to constrain.

(See exercise 8.)