Tikhonov Regularization - Regularization in Hilbert Space

Regularization in Hilbert Space

Typically discrete linear ill-conditioned problems result from discretization of integral equations, and one can formulate a Tikhonov regularization in the original infinite dimensional context. In the above we can interpret as a compact operator on Hilbert spaces, and and as elements in the domain and range of . The operator is then a self-adjoint bounded invertible operator.