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# program1 - Program 1 Foundations of Computational Math 2...

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Unformatted text preview: Program 1 Foundations of Computational Math 2 Spring 2011 Due date: 11:59 PM Monday, 2/7/11 via email Problem 1.1 Assume you are given distinct points x , . . . , x n , and a function f ( x ). 1.1.a . Implement a routine that computes the divided difference table given the data ( x , f ( x )) , . . . , ( x n , f ( x n )). 1.1.b . Implement a routine that evaluates the Newton form of the interpolating poly- nomial at any value x . Make sure that you implement an efficient algorithm with O ( n ) computational complexity. This can be done by modifying the idea of Horner’s rule. 1.1.c . In addition to the value x , this routine should take as input some specification of the path through the table that is to be used for the evaluation of p n ( x ). This path should be specified as a sequence of integers listing the indices of the points in the order they should be included in the form of the Newton poly- nomial. For example, if you have a divided difference table built for the pairs ( x , f...
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program1 - Program 1 Foundations of Computational Math 2...

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