Saddle point problem and a note to its preconditioning

Preconditioning techniques form an crucial part of developing efficient solvers for saddle point problems, and are often conjugated with Krylov's subspace methods. One saddle point system can be arisen from discretisation of a thin plate spline which is a popular data fitting technique. Such a system is problematic with respect to its conditioning. Some common saddle point preconditioners are considered, and a note of finding preconditioner will be mentioned from Gergelits et.al. recent work.