Changes between Version 5 and Version 6 of u/erica/norms

Timestamp:

08/22/13 15:48:48 (11 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/norms

@@ -39 +39 @@
 2-norm:
 
-[[latex($||e||_2 = \sum_{i=1} ^{s}(|e_i|^2)^{1/2} $)]], and
+[[latex($||e||_2 = \sum_{i=1} ^{s}\sqrt{|e_i|^2} $)]], and
 
 infinity-norm:
@@ -53 +53 @@
 = Error of functions = 
 
-Some methods produce approximate ''functions'', U(x), to some analytical or true function, u(x). The error now is given by e(x) = U(x)-u(x). To measure the norm of this error over the interval of the solution, we can consider the 3 norms of the previous section but now using integrals over the interval (rather than sums over the vector components). 
+Some methods produce approximate ''functions'', U(x), to some analytical or true function, u(x). The error now is given by e(x) = U(x)-u(x). To measure the norm of this error over the interval of the solution, we can consider the 3 norms of the previous section but now using integrals over the interval (rather than sums over the vector components):
+
+[[latex($||e||_1 = \int^b_a|e(x)| dx $)]]
+
+[[latex($||e||_2 = \sqrt{\int^b_a|e(x)|^2 dx} $)]]
+
+[[latex($||e||_{\infty} = max_{(a\leq x\leq b)} |e(x)| $)]]