Meurant, Gérard The computation of bounds for the norm of the error in the conjugate gradient algorithm. (English) Zbl 0897.65026 Numer. Algorithms 16, No. 1, 77-87 (1997). The computation of bounds for the norm of the error in the conjugate gradient algorithm is considered. Section 2 recalls how to compute approximations of the A-norm and shows these approximations are lower and upper bounds. Section 3 shows how to compute approximations of the \(l_2\)-norm. Section 4 introduces an adaptive algorithm that computes estimates of the smallest eigenvalue that is needed to obtain upper bounds of the norm. Some numerical experiments showing the effectiveness of this approach are given in the last section. Reviewer: Xie Shenquan (Xiangtan) Cited in 20 Documents MSC: 65F10 Iterative numerical methods for linear systems 65F50 Computational methods for sparse matrices Keywords:error bounds; extreme eigenvalues; conjugate gradient algorithm; adaptive algorithm; numerical experiments PDFBibTeX XMLCite \textit{G. Meurant}, Numer. Algorithms 16, No. 1, 77--87 (1997; Zbl 0897.65026) Full Text: DOI