# Numerical analysis question.

1. Nov 1, 2006

### angel23

in newton forward differece method.
how can i know that i reached the best interpolation????

for example in a function like sqrt(x) for Xi=1,1.05,1.10,1.15,1.20,1.25,1.3

the best interpolation is at P3(x) why???how can i know???
this really makes me conused

if anyone helped me i will be grateful

2. Nov 29, 2006

### dashing

in newton forward differece method.

Asalam o Alikum

Mr ,
Value of f(x) at that point define you where the best interpolation between the point is exsist

3. Dec 26, 2006

### xhatemx

simply you construct the table and you will find for this example that after certain iteration the numbers in a certain column will be the same or of accuracy better than that required by the question. this is when you stop . .

4. Dec 26, 2006

### HallsofIvy

Staff Emeritus
What do you mean by "best"? There exist an infinite number of, say, cubic polynomials that interpolate the points you give. One possible definition of "best" is that $\Sigma |f(x_i)- y_i|$ be a minimum. Another is $Max |f(x_i)- y_i|$ be a minimum and yet another is that $\sqrt{\int (f(x_i)- y_i)^2 dx}$ be a minimum. Each of those has applications.

5. Dec 29, 2006

### ssd

Very true sir, I was just going to mention the same.

6. Feb 21, 2007

### angel23

:) it is too late, sir i got my answer once i posted the question.(it is too late all)

any way thanks.