Restrictions and Max Error Estimate ●Restrictions function slices x-axis at root start with two points a and b f(a)f(b)<0 graphing tool (e.g.,Matlab)can help to find a and b require co[a,(why?note:not a big deal) ●Max error estimate after n steps,guess midpoint of current range *error::e≤2n号((think of=0,1,2) note:error is in x;can also look at error in f(x)or combination enters entire world of stopping criteria Question:Given tolerance (in z),what is n?... Copyright©2011，NA⊙Yin Last Modification:Oct.2011 Restrictions and Max Error Estimate • Restrictions ∗ function slices x-axis at root ? start with two points a and b 3 f(a)f(b) < 0 ? graphing tool (e.g., Matlab) can help to find a and b ∗ require C 0 [a, b] (why? note: not a big deal) • Max error estimate ∗ after n steps, guess midpoint of current range ∗ error:  ≤ b−a 2n+1 (think of n = 0, 1, 2) ∗ note: error is in x; can also look at error in f(x) or combination ? enters entire world of stopping criteria Question: Given tolerance (in x), what is n? · · · Copyright c 2011, NAYin Last Modification: Oct. 2011 7