This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: functions deﬁned over the interval [ a,b ]. (b) Derive an error expression similar to (1) for the formula you obtain in (a). 5. Consider the ﬁxed point iteration x n +1 = F ( x n ) 1 (a) Assume that the ﬁxed point iteration converges, explicitly derive the conditions on F that ensure a second order rate of convergence. (b) Using your result from (a), derive the condition on φ ( x ) so that the iteration x n +1 = x n + φ ( x n ) f ( x n ) will have a second order rate of convergence to a root α of the problem f ( x ) = 0. 6. Assume the points { x i } , for i = 1 , 2 ,...,n + 1, are distinct. Prove that the polynomial of degree ≤ n that interpolates the data { ( x i ,y i ) } is unique. 2...
View
Full Document
 Spring '11
 NA
 Numerical Analysis, imized., ck qk

Click to edit the document details