A conjugate-gradient-type rational Krylov subspace method for ill-posed problems

Abstract

Conjugated gradients on the normal equation (CGNE) is a popular method to regularise linear inverse problems. The idea of the method can be summarised as minimising the residuum over a suitable Krylov subspace. It is shown that using the same idea for the shift-and-invert rational Krylov subspace yields an order-optimal regularisation scheme.

References in corpus (1)

• Automatic smoothness detection of the resolvent Krylov subspace method for the approximation of $C_0$-semigroups

Cited by in corpus (1)

• An extended Krylov subspace method for decoding edge-based compressed images by homogeneous diffusion