This paper discusses the use of the L-curve in the regularization of discrete ill-posed problems. Regularization algorithms are used to produce reasonable solutions to ill-posed problems, where the L-curve is a plot of the size of the regularized solution versus the size of the corresponding residual for all valid regularization parameters. The paper establishes two main results: first, a unifying characterization of various regularization methods is given, showing that the measurement of "size" depends on the particular regularization method. For example, the 2-norm is appropriate for Tikhonov regularization, while a 1-norm in the coordinate system of the singular value decomposition (SVD) is relevant to truncated SVD regularization. Second, a new method is proposed for choosing the regularization parameter based on the L-curve, which is shown to be more robust in the presence of correlated errors compared to generalized cross validation. The paper also discusses the properties of the L-curve, showing that it has an L-shaped appearance, with a distinct corner where the solution changes from being dominated by regularization errors to being dominated by the errors in the right-hand side. The L-curve method for choosing the regularization parameter has advantages over generalized cross validation, as the computation of the corner is a well-defined numerical problem and the method is rarely "fooled" by correlated errors. The paper also presents numerical examples demonstrating the effectiveness of the L-curve method in choosing the regularization parameter. The results show that the L-curve method is more robust than generalized cross validation, particularly in the presence of correlated errors. The paper concludes that the L-curve method is a useful tool for choosing the regularization parameter in ill-posed problems.This paper discusses the use of the L-curve in the regularization of discrete ill-posed problems. Regularization algorithms are used to produce reasonable solutions to ill-posed problems, where the L-curve is a plot of the size of the regularized solution versus the size of the corresponding residual for all valid regularization parameters. The paper establishes two main results: first, a unifying characterization of various regularization methods is given, showing that the measurement of "size" depends on the particular regularization method. For example, the 2-norm is appropriate for Tikhonov regularization, while a 1-norm in the coordinate system of the singular value decomposition (SVD) is relevant to truncated SVD regularization. Second, a new method is proposed for choosing the regularization parameter based on the L-curve, which is shown to be more robust in the presence of correlated errors compared to generalized cross validation. The paper also discusses the properties of the L-curve, showing that it has an L-shaped appearance, with a distinct corner where the solution changes from being dominated by regularization errors to being dominated by the errors in the right-hand side. The L-curve method for choosing the regularization parameter has advantages over generalized cross validation, as the computation of the corner is a well-defined numerical problem and the method is rarely "fooled" by correlated errors. The paper also presents numerical examples demonstrating the effectiveness of the L-curve method in choosing the regularization parameter. The results show that the L-curve method is more robust than generalized cross validation, particularly in the presence of correlated errors. The paper concludes that the L-curve method is a useful tool for choosing the regularization parameter in ill-posed problems.