<html><head><meta http-equiv="Content-Type" content="text/html; charset=us-ascii"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class=""><br class=""></div> This is discussed in <a href="https://petsc.org/release/docs/manual/ksp/" class="">https://petsc.org/release/docs/manual/ksp/</a> you can see the exact formulas in the code at <a href="https://petsc.org/release/src/ksp/ksp/interface/iterativ.c.html#KSPConvergedDefault" class="">https://petsc.org/release/src/ksp/ksp/interface/iterativ.c.html#KSPConvergedDefault</a><div class=""><br class=""></div><div class=""> If one uses a nonzero initial guess then there are two choices for the initial residual definition, either the residual at the initial guess or the right hand side for the problem see KSPConvergedDefaultSetUIRNorm</div><div class=""><br class=""></div><div class=""> Barry</div><div class=""><br class=""><div><br class=""><blockquote type="cite" class=""><div class="">On Jan 6, 2022, at 1:52 PM, Ning Li <<a href="mailto:ning.li@simtechnologyus.com" class="">ning.li@simtechnologyus.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><meta charset="UTF-8" class=""><div class="WordSection1" style="page: WordSection1; caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;"><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Hello,<o:p class=""></o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">I am trying to compare PETSc and Lis libraries.<span class="Apple-converted-space"> </span><br class=""><br class="">In PETSc I could use absolute or relative tolerance. I want to know what is your definition of relative tolerance?<br class=""><br class="">In Lis, they have 3 convergence conditions:<br class=""><span id="cid:image001.png@01D802FC.1A405EF0"><image001.png></span><o:p class=""></o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Thanks<span class="Apple-converted-space"> </span><o:p class=""></o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Ning Li</div></div></div></blockquote></div><br class=""></div></body></html>