<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><br><div><div>On 2010/04/12, at 1:28 AM, Matthew Knepley wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div dir="ltr">Someone has gone the extra mile and made an A-orthogonal Lanczos<div><br></div><div> <a href="http://arxiv.org/pdf/1004.1622v1">http://arxiv.org/pdf/1004.1622v1</a></div></div></blockquote><div><br></div>Is that hard? Basically a slightly different inner product. A-orthogonalization gives L2 minimal residuals. (Under the ordinary inner product the residuals are minimal in the A^{-1} norm)</div><div><br><blockquote type="cite"><div dir="ltr"><div>It appears to outperform BiCGStab in enough of their tests</div></div></blockquote><br><div><br></div>That might be true since BiCGS is based on the ordinary Lanczos / BiCG.</div><div><br></div><div>Hm. Why not do an A-orthogonal BicGstab. Hold on. Let me grab some scrap paper.....</div><div><br></div><div>Victor.</div><div><br><blockquote type="cite"><div dir="ltr"><div><br> </div></div></blockquote></div><br><div apple-content-edited="true"> <span class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><div style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; "><span class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><div>-- </div><div>Victor Eijkhout -- 865 974 9308</div><div>eijkhout@cs.utk.edu <a href="http://www.cs.utk.edu/~eijkhout/">http://www.cs.utk.edu/~eijkhout/</a></div><div><br class="khtml-block-placeholder"></div><br class="Apple-interchange-newline"></span></div></span> </div><br></body></html>