Extrapolation techniques for ill-conditioned linear systems (Q1279834)

The authors develop vector rational extrapolation techniques and apply them to regularized solutions of the ill-conditioned system \(Ax=b\) computed for several values of the regularization parameter \(\lambda\) in order to extrapolate these solutions at \(\lambda=0\). The extrapolation procedures are based on the behaviour of \(x_\lambda= \arg\min_x J(\lambda,x)\) \((J\) is the Tikhonov functional) with respect to \(\lambda\). The effectiveness of the procedures is illustrated numerically.