Analysis of discrete ill-posed problems by means of the L-curve.

*(English)*Zbl 0770.65026This paper is concerned with the parameter choice problem in regularization methods for linear ill-posed problems. A convenient way for studying this problem is to plot - for various regularization parameters - the (semi)norm of the regularized solution versus the norm of the corresponding residual. Using logarithmic scales on both axes, this plot typically exhibits a shape like an “\(L\)”, hence its name \(L\)- curve. The author provides several model computations, perturbation bounds and heuristic arguments to advocate that a ”good“ regularization parameter is one close to the right of the \(L\)’s corner (\(L\)-curve criterion). Numerical experiments support the author’s opinion. Unfortunately, it remains an open question under what conditions the reconstructions with the \(L\)-curve criterion will improve when the noise- level in the data is reduced towards zero.

Reviewer: Martin Hanke

##### MSC:

65F20 | Numerical solutions to overdetermined systems, pseudoinverses |

65F30 | Other matrix algorithms (MSC2010) |