Tikhonov regularization

Summary

Tikhonov regularization is a method to solve an ill-posed linear equation $K x = y$ in a stable way. Instead of solving the equation, it minimizes $\norm{K x - y}^2 + \alpha \norm{x}^2$ for a small parameter $\alpha > 0$. The minimizer always exists, is unique, and depends continuously on the data $y$. It is the standard tool for inverse problems such as first-kind integral equations, and in statistics it is known as ridge regression.