On Error Estimation in the Conjugate Gradient Method and why it Works in Finite Precision Computations

0404211 - UIVT-O 20020143 RIV US eng J - Journal Article
Strakoš, Zdeněk - Tichý, Petr
On Error Estimation in the Conjugate Gradient Method and why it Works in Finite Precision Computations.
Electronic Transactions on Numerical Analysis. Roč. 13, - (2002), s. 56-80. ISSN 1068-9613. E-ISSN 1068-9613
R&D Projects: GA ČR GA201/02/0595
Institutional research plan: AV0Z1030915
Keywords : conjugate gradient method * Gauss kvadrature * evaluation of convergence * error bounds * finite precision arithmetic * rounding errors * loss of orthogonality
Subject RIV: BA - General Mathematics
Impact factor: 0.565, year: 2002
http://etna.mcs.kent.edu/volumes/2001-2010/vol13/abstract.php?vol=13&pages=56-80

This paper shows that the lower bound for the A-norm of the error based on Gauss quadrature is mathematically equivalent to the formula given by Hestenes and Stiefel. It compares existing bounds and demonstrates necessity of a proper rounding error analysis. It is given an example of the well-known bound which can fail in finite precision arithmetic. The simplest bound is proved numerically stable. Results are illustrated by numerical experiments.
Permanent Link: http://hdl.handle.net/11104/0124477