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# hw1 - Homework 1 Foundations of Computational Math 2 Spring...

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Homework 1 Foundations of Computational Math 2 Spring 2011 Solutions will be posted Monday, 1/17/11 Written homework problems are study questions. You need not turn in solutions but you are strongly encouraged to do the problems and read the posted solutions carefully. Problem 1.1 Consider the data points ( x,y ) = { (0 , 2) , (0 . 5 , 5) , (1 , 8) } Write the interpolating polynomial in both Lagrange and Newton form for the given data. Problem 1.2 Use this divided difference table for this problem. Justify all of your answers. i 0 1 2 3 4 5 x i 1 0 2 4 5 6 f i 13 2 14 18 67 91 f [ , ] 11 8 16 49 24 f [ , , ] 1 6 11 25 / 2 f [ , , , ] 1 1 47 / 8 f [ , , , , ] 0 55 / 48 f [ , , , , , ] 55 / 336 1.2.a Use the divided difference information about the unknown function f ( x ) and consider the unique polynomial, denoted p 1 , 5 ( x ), that interpolates the data given by pairs ( x 1 ,f 1 ), ( x 2 ,f 2 ), ( x 3 ,f 3 ), ( x 4 ,f 4 ) , and ( x 5 ,f 5 ). Use two different sets of divided differences to express p 1 , 5 ( x ) in two distinct forms.

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