This function inverts ill conditioned matrices using an iterative solution to the Tikhonov regularization problem. It takes three arguments: A, the matrix, l, lambda the contraint, and k, the number of iterations. In this iterative Tikhonov regularization model, also known as ridge regression, I introduce an iterative solution to the ill-posed linear inverse problem. My approach to the inverse problem can be viewed as a generalization of existing methods, where, in addition to the regularization parameter, I introduce a second regularization parameter as the number if iterations. This work is motivated by the fact that the least squares solution does not give a reasonable result when the data matrix is singular or ill-conditioned. Test cases show that the approach is either better or significantly better than existing L2 regularization methods.