Arnoldi is converging very nicely for you so the condition number is likely 3.something
You can run with -ksp_rtol 1.e-13 -ksp_gmres_restart 50 to get tighter convergence. Barry On Mar 14, 2011, at 1:16 AM, Gong Ding wrote: > Hi, > I use -ksp_monitor_singular_value to view the approximate condition number of > my matrix. > The output during the GMRES iteration looks like > > 0 KSP Residual norm 1.072677079362e+02 % max 1 min 1 max/min 1 > 1 KSP Residual norm 2.558517256216e+01 % max 0.949986 min 0.949986 max/min > 1 > 2 KSP Residual norm 7.952391160495e+00 % max 1.00443 min 0.53867 max/min > 1.86465 > 3 KSP Residual norm 3.147058569003e+00 % max 1.01529 min 0.418892 max/min > 2.42375 > 4 KSP Residual norm 1.213876539809e+00 % max 1.04559 min 0.365424 max/min > 2.86131 > 5 KSP Residual norm 4.398018777420e-01 % max 1.0717 min 0.341344 max/min > 3.13966 > 6 KSP Residual norm 1.681000721101e-01 % max 1.07182 min 0.333065 max/min > 3.21806 > 7 KSP Residual norm 6.008534584667e-02 % max 1.07287 min 0.330693 max/min > 3.24432 > 8 KSP Residual norm 2.317545636598e-02 % max 1.07476 min 0.32966 max/min > 3.26019 > 9 KSP Residual norm 8.732395511044e-03 % max 1.0798 min 0.32928 max/min > 3.27929 > 10 KSP Residual norm 3.543098250574e-03 % max 1.08891 min 0.328903 max/min > 3.31073 > 11 KSP Residual norm 1.322114569421e-03 % max 1.1002 min 0.328779 max/min > 3.34632 > 12 KSP Residual norm 4.278882091191e-04 % max 1.12562 min 0.328666 max/min > 3.4248 > 13 KSP Residual norm 1.503136522978e-04 % max 1.13558 min 0.328572 max/min > 3.45611 > 14 KSP Residual norm 5.410712876997e-05 % max 1.1531 min 0.32832 max/min > 3.51211 > 15 KSP Residual norm 2.200160155820e-05 % max 1.16627 min 0.328089 max/min > 3.55474 > 16 KSP Residual norm 9.689610704862e-06 % max 1.17549 min 0.327714 max/min > 3.58694 > 17 KSP Residual norm 4.077334723619e-06 % max 1.18316 min 0.32763 max/min > 3.61126 > 18 KSP Residual norm 1.522015252918e-06 % max 1.18949 min 0.327542 max/min > 3.63158 > > > In the first iteration, the min and max singular value are both 1, and the > ratio of max/min increase quickly > in the next iterations. > >> From above values, how to extract the condition number of (preconditioned) >> matrix? >
