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 ?

  • $\begingroup$ 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


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.