On rules for stopping the conjugate gradient type methods in ill‐posed problems

Abstract

We consider stopping rules in conjugate gradient type iteration methods for solving linear ill‐posed problems with noisy data. The noise level may be known exactly or approximately or be unknown. We propose several new stopping rules, mostly for the case of unknown noise level. Numerical comparison with known rules (discrepancy principle, montone error rule, L‐curve rule, Hanke‐Raus rule) shows that the new rules are competitive. First Published Online: 14 Oct 2010

Keywords

• Ill‐posed problems
• conjugate gradient type iteration methods
• noise level
• stopping rule
• discrepancy principle
• monotone error rule