June 6th, 2017, 09:12 AM  #1 
Newbie Joined: Jun 2017 From: France Posts: 3 Thanks: 0  Neville algorithm
Hello, I post this message because in the following exercise I am asked to use the Neville algorithm, and I do not know exactly how to use it and whether I have the right formula. Here is this exercise: Let f be a real function whose value is known in 5 points: 0 <= i <= 4 xi = { 1,1,1,2,3}, f (xi) is equivalent to fi = {8, 2,2,1,5} And I'm asked to use the Neville algorithm to compute an approximate value of f (1/2) and f (1/2). The formula that I find is not first of this site "http://www.uvt.rnu.tn/resourcesuvt/cours/analyse_num/chap4/node4.html" The P represents a polynomial normally. Can anyone help me please? Last edited by skipjack; June 6th, 2017 at 10:21 PM. 
June 6th, 2017, 10:33 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 17,919 Thanks: 1386  
June 7th, 2017, 03:59 AM  #3 
Newbie Joined: Jun 2017 From: France Posts: 3 Thanks: 0 
Yes,sorry it's xi={1,0,1,2,3}!

June 17th, 2017, 04:11 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,653 Thanks: 681 
So you have f(1)= 8, f(0)= 2, f(1)= 2, f(2)= 1, f(3)= 5. "Neville's algorithm" is basically a "divided difference" method using Newton's difference formula. , , , and . Then , , and . , and . . "Newton's difference formula" says that we can approximate f(x) by . 

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