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A. Greenbaum, “Behavior of Slightly Perturbed Lanczos and Conjugate-Gradient Recurrences,” Linear Algebra and its Applications, Vol. 113, 1989, pp. 7-63.

has been cited by the following article:

• TITLE: On the Behavior of the Residual in Conjugate Gradient Method

  AUTHORS: Teruyoshi Washizawa

  KEYWORDS: Conjugate Gradient, Residual, Convergence, Finite Arithmetic, Lower Bound

  JOURNAL NAME: Applied Mathematics, Vol.1 No.3, September 29, 2010

  ABSTRACT: In conjugate gradient method, it is well known that the recursively computed residual differs from true one as the iteration proceeds in finite arithmetic. Some work have been devoted to analyze this behavior and to evaluate the lower and the upper bounds of the difference. This paper focuses on the behavior of these two kinds of residuals, especially their lower bounds caused by the loss of trailing digit, respectively.