Abstract
The L-curve is a popular aid for determining a suitable value of the regularization parameter when solving ill-conditioned linear systems of equations with a right-hand side vector, which is contaminated by errors of unknown size. However, for large problems, the computation of the L-curve can be quite expensive, because the determination of a point on the L-curve requires that both the norm of the regularized approximate solution and the norm of the corresponding residual vector be available. Recently, an approximation of the L-curve, referred to as the L-ribbon, was introduced to address this difficulty. The present paper discusses how to organize the computation of the L-ribbon when the matrix of the linear system of equations has many more columns than rows. Numerical examples include an application to computerized tomography.
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Calvetti, D., Morigi, S., Reichel, L. et al. An L-ribbon for large underdetermined linear discrete ill-posed problems. Numerical Algorithms 25, 89–107 (2000). https://doi.org/10.1023/A:1016656923184
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DOI: https://doi.org/10.1023/A:1016656923184