On Error Estimation in the Conjugate Gradient Method: Normwise Backward Error

0458346 - ÚI 2017 RIV SK eng C - Conference Paper (international conference)
Tichý, Petr
On Error Estimation in the Conjugate Gradient Method: Normwise Backward Error.
Algoritmy 2016. Bratislava: Slovak University of Technology, 2016 - (Handlovičová, A.; Ševčovič, D.), s. 323-332. ISBN 978-80-227-4544-4.
[ALGORITMY 2016. Conference on Scientific Computing /20./. Vysoké Tatry - Podbanské (SK), 13.03.2016-18.03.2016]
R&D Projects: GA ČR GA13-06684S
Institutional support: RVO:67985807
Keywords : conjugate gradients * normwise backward error * incremental norm estimation
Subject RIV: BA - General Mathematics

Using an idea of Duff and Vömel [BIT, 42 (2002), pp. 300-322 ] we suggest a simple algorithm that incrementally estimates the 2-norm of Jacobi matrices that are available during the conjugate gradient (CG) computations. The estimate can be used, e.g., in stopping criteria based on the normwise backward error. Numerical experiments predict that the estimate approximates the 2-norm of A with a suffcient accuracy.
Permanent Link: http://hdl.handle.net/11104/0258611