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        Dear PETSC moderator,
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        I found there are classical and modified gram-schmidt options for KSPGMRES solver. For classical GS, one could define
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        additional orthogonalization sweeps, while for modified GS there is no such option. I got the impression that PETSC
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        GMRES implementation assumes that the MGS is so robust that double orthogonalization is unnecessary. However, our
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        recent experience indicated that even for MGS, double orth. is nenecessary. Otherwise, GMRES would produce an increase
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        residual convergence history. 
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        I'm emailing for clarification on this: was it because I did not use the option correctly with some misunderstanding
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        about the user guide, or is this indeed the current situation for the KSPGMRES solver implemention?
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        As a side note, it was written in Yousef Saad's book 'Iterative methods for sparse linear systems, second editon' 
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        (page 162) that
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        <span style="color:#E53333;font-family:Times-Roman;font-size:14px;" class="ke-content-forecolor"><span style="font-family:SimSun;">"However,
there are cases where cancellations are so severe in the orthogonalization steps that
even</span></span>
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        <span style="color:#E53333;font-family:Times-Roman;font-size:14px;" class="ke-content-forecolor"><span style="font-family:SimSun;">the Modified Gram-Schmidt option is inadequate</span>." </span>It seems that Prof Saad was well aware of this, which backs
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        our finding.
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        Thanks and look forward to further discussion on this.
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        Best regards,
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        Shenren
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        徐慎忍<br>
西北工业大学动力与能源学院 副教授/博导<br>
手机/微信：18762660364<br>
电子邮箱：shenren_xu@nwpu.edu.cn<br>
个人主页：<a href="https://urldefense.us/v3/__https://teacher.nwpu.edu.cn/xushenren.html__;!!G_uCfscf7eWS!ZQPNzqIpQl_f9D2grHzxnPVMeys4fV6pumRzr-GoGSdYnvlc6af7refw2J_yHEC2AJewkzY4oRv6Z4fmyMum0-iAy1Lk4Q$">https://teacher.nwpu.edu.cn/xushenren.html</a>
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        Shenren Xu, PhD<br>
Associate Professor<br>
School of Power and Energy<br>
Northwestern Polytechnical University<br>
Xi'an 710129 , China P.R.<br>
Tel: +86-18762660364<br>
Web: <a href="https://urldefense.us/v3/__https://teacher.nwpu.edu.cn/xushenren.html__;!!G_uCfscf7eWS!ZQPNzqIpQl_f9D2grHzxnPVMeys4fV6pumRzr-GoGSdYnvlc6af7refw2J_yHEC2AJewkzY4oRv6Z4fmyMum0-iAy1Lk4Q$">https://teacher.nwpu.edu.cn/xushenren.html</a><br>
Email: shenren_xu@nwpu.edu.cn
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