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I'm looking for an alternative formulation of Quasi-Minimal Residual (QMR) from Freund and Nachtigal (1994) based on a Lanczos process for complex valued matrices based on $A^H$ instead of $A^T$.

Specifically, I'm not quite sure how algorithm 7.1 would change if one where to use $A^H$ instead of $A^T$. Is there some article or book where I can find such a QMR formulation ?

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  • $\begingroup$ I assume you are talking about QMR applied to a complex-valued matrix. Can you confirm that Lanczos process in the formulation you are interested actually uses $A^H$ instead of $A^T$ for complex-valued matrices? (as it is quite usual to present the method for real-valued matrices and use a simple transpose operator while implying that a conjugate-transpose is applied when $A\in\mathbb C$) $\endgroup$
    – Anton Menshov
    Commented Jan 12, 2023 at 0:08
  • $\begingroup$ Yes, my matrix $A$ is complex-valued. I'm going to edit my question to make it clearer $\endgroup$ Commented Jan 12, 2023 at 8:00

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