Estimation of the \(L\)-curve via Lanczos bidiagonalization
A new approach is proposed to determine a value of the regularization parameter in solving ill-conditioned systems of linear equations with a right-hand side contamined by errors of unknown norm. The approach is based on computing an \(L\)-ribbon that contains the \(L\)-curve in its interior. An \(L\)-ribbon can be computed inexpensively by partial Lanczos bidiagonalization of the matrix of the given system of equations. A suitable value of the regularization parameter is then determined from the \(L\)-ribbon, and it is shown that an associated approximate solution of the linear system can be computed with little additional work.
ill-conditioned systems of linear equations
scientific article; zbMATH DE number 1398423