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Unformatted text preview: functions dened over the interval [ a,b ]. (b) Derive an error expression similar to (1) for the formula you obtain in (a). 5. Consider the xed point iteration x n +1 = F ( x n ) 1 (a) Assume that the xed 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 ( x ) so that the iteration x n +1 = x n + ( x n ) f ( x n ) will have a second order rate of convergence to a root 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...
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This note was uploaded on 06/19/2011 for the course MATH 684 taught by Professor Na during the Spring '11 term at University of North Carolina School of the Arts.
 Spring '11
 NA
 Numerical Analysis

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