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The use of the CADNA library for validating the numerical results of the hybrid GMRES algorithm
Applied Numerical Mathematics, 1997 The author shows that the hybrid GMRES algorithm of \textit{N. M. Nachtigal}, \textit{L. Reichel} and \textit{L. N. Trefethen} [SIAM J. Matrix Anal. Appl. 13, No. 3, 796-825 (1992; Zbl 0757.65035)] may fail due to properties of floating-point arithmetic. In these cases either the result is false or spoiled by serious round-off errors.
F. Toutounian
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