Tikhonov regularization and the L-curve for large discrete ill-posed problems
The problem is to solve very ill-conditioned large systems of linear algebraic equations obtained by discretization of linear inverse problems. For solving such ill-posed problems the Tikhonov regularization method is used. The total cost of an regularization method is to a large extent determined by the amount of the computational work needed for determining a suitable regularization parameter. The authors survey available iterative methods, and develope new ones, based on the L-curve method, in particular, on the L-ribbon method for the determination a proper value for the regularization parameter. They discuss iterative methods based on the Laczos bidiagonalization and the Arnoldi process for the computation of approximate values for \(\mu\) that corresponds to the value of the regularization parameter obtainable by the L-curve criterion. Computed examples are presented.
ill-conditioned large systems of linear algebraic equations
scientific article; zbMATH DE number 1546557
scientific article