an:05033445
Zbl 1092.65025
Morigi, S.; Reichel, L.; Sgallari, F.; Zama, F.
Iterative methods for ill-posed problems and semiconvergent sequences
EN
J. Comput. Appl. Math. 193, No. 1, 157-167 (2006).
00126225
2006
j
65F10 65F22
iterative method; stopping criterion; L-curve; large-scale ill-posed problems; semiconvergent sequences; asymptotic expansions
Summary: 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.