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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The minimal error conjugate gradient method is a regularization method
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by Martin Hanke PDF
Proc. Amer. Math. Soc. 123 (1995), 3487-3497 Request permission

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
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 3487-3497
  • MSC: Primary 65J10; Secondary 47A50, 65J20
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1285994-5
  • MathSciNet review: 1285994