Tikhonov regularization and the L-curve for large discrete ill-posed problems

[摘要] Discretization of linear inverse problems generally gives rise to very ill-conditioned linear systems of algebraic equations. Typically, the linear systems obtained have to be regularized to make the computation of a meaningful approximate solution possible. Tikhonov regularization is one of the most popular regularization methods. A regularization parameter specifies the amount of regularization and, in general, an appropriate value of this parameter is not known a priori. We review available iterative methods, and present new ones, for the determination of a suitable value of the regularization parameter by the L-curve criterion and the solution of regularized systems of algebraic equations. (C) 2000 Elsevier Science B.V. All rights reserved.

[发布日期] 2000-11-01

[关键词] ill-posed problem;regularization;L-curve criterion;Gauss quadrature