Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
Journal of the ACM (JACM)
The triangle method for finding the corner of the L-curve
Applied Numerical Mathematics
Numerical Methods
A new L-curve for ill-posed problems
Journal of Computational and Applied Mathematics
Greedy Tikhonov regularization for large linear ill-posed problems
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
Old and new parameter choice rules for discrete ill-posed problems
Numerical Algorithms
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Iterative schemes, such as LSQR and RRGMRES, are among the most efficient methods for the solution of large-scale ill-posed problems. The iterates generated by these methods form semiconvergent sequences. A meaningful approximation of the desired solution of an ill-posed problem often can be obtained by choosing a suitable member of this sequence. However, it is not always a simple matter to decide which member to choose. Semiconvergent sequences also arise when approximating integrals by asymptotic expansions, and considerable experience and analysis of how to choose a suitable member of a semiconvergent sequence in this context are available. The present note explores how the guidelines developed within the context of asymptotic expansions can be applied to iterative methods for ill-posed problems.