The minimal error conjugate gradient method is a regularization method

Author:
Martin Hanke

Journal:
Proc. Amer. Math. Soc. **123** (1995), 3487-3497

MSC:
Primary 65J10; Secondary 47A50, 65J20

MathSciNet review:
1285994

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Abstract: The regularizing properties of the conjugate gradient iteration, applied to the normal equation of a linear ill-posed problem, were established by Nemirovskii in 1986. A seemingly more attractive variant of this algorithm is the minimal error method suggested by King. The present paper analyzes the regularizing properties of the minimal error method. It is shown that the discrepancy principle is no regularizing stopping rule for the minimal error method. Instead, a different stopping rule is suggested which leads to order-optimal convergence rates.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1995-1285994-5

Keywords:
Linear ill-posed problems,
iterative regularization,
conjugate gradients,
minimal error method,
discrepancy principle,
oder-optimal error bounds

Article copyright:
© Copyright 1995
American Mathematical Society