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.
Calvetti, D., Morigi, S., Reichel, L., Sgallari, F. (2000). An L-ribbon for large underdetermined linear discrete ill-posed problems. NUMERICAL ALGORITHMS, 25(1-4), 89-107 [10.1023/a:1016656923184].
An L-ribbon for large underdetermined linear discrete ill-posed problems
Morigi S.;Reichel L.;Sgallari F.
2000
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.