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Can you suggest me a reference (besides Wikipedia) where the GMRES (Generalized minimal residual method) algorithm is explained in full detail, in a nice and easy way to understand? A clearly written, easy to follow resource would be wonderful.

Thank you very much for your time!

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It was developed by Yousef Saad and Martin Schultz. It can be found in Saad's book, chapter 6.5.

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    Thank you, will look into all the posted resources and report back.2012-08-18
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Bau and Trefethen's Numerical linear algebra is a very enjoyable read.

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    But this book doesn't appear to have a good handle on GMRES. I couldn't understand how to form $Q_n$ out of $Q_{n-1}$ at the $n$-th step of Arnoldi iteration.2018-12-07