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

• ID: 2738, RIV: 10331478
• ISSN: not specified, ISBN: 978-80-227-4544-4
• source: Proceedings of the Conference Algoritmy 2016
• keywords: conjugate gradients; normwise backward error; incremental norm estimation
• authors: Petr Tichý
• authors from KNM: not assigned

Abstract

Using an idea of Duff and Vomel [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. A numerical experiment predicts that the estimate approximates the 2-norm of A with a sufficient accuracy.