Iterative methods for ill-posed problems and semiconvergent sequences

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Abstract

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. © 2005 Elsevier B.V. All rights reserved.

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Morigi, S., Reichel, L., Sgallari, F., & Zama, F. (2006). Iterative methods for ill-posed problems and semiconvergent sequences. Journal of Computational and Applied Mathematics, 193(1), 157–167. https://doi.org/10.1016/j.cam.2005.05.028

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