Changes between Version 11 and Version 12 of u/erica/norms

Timestamp:

08/26/13 11:31:47 (11 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/norms

@@ -78 +78 @@
 [[latex($||e||_{\infty} = max_{(1\leq i\leq mx)} |e_i| $)]]
 
-Now, we see that the error explicitly contains h, and so the equivalence of the different norms is now broken as one varies mx. Also, there seems to be a nice interpretation of e1, it is the average error over the grid (times the length of the grid). 
+Now, we see that the error explicitly contains h, and so the equivalence of the different norms is potentially broken as one varies mx. It can be shown that this applies when the solution has kinks in it, but for sufficiently smooth solution, the different norms produce similar convergence rates. Also, there seems to be a nice interpretation of e1, it is the average error over the grid (times the length of the grid). 
 
 = Summary =