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June 6th, 2017, 10:12 AM   #1
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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/resources-uvt/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 11:21 PM.
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June 6th, 2017, 11:33 PM   #2
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Quote:
Originally Posted by Joan94 View Post
0 <= i <= 4 xi = {- 1,1,1,2,3}, f (xi) is equivalent to fi = {8, -2,2,1,5}
Should you have typed "xi = {- 1,0,1,2,3}" instead of "xi = {- 1,1,1,2,3}"?
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June 7th, 2017, 04:59 AM   #3
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Yes,sorry it's xi={-1,0,1,2,3}!
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June 17th, 2017, 05:11 AM   #4
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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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