math translation (Now scanned)

[Reel]

Ok, I have this problem to do and I can't even begin to figure out what it means: (sub will be represented by _)

Construct a sequence of interpolating values y_n to f(1 + sqrt(10)) where f(x) = 1/(1+ x^2) for -5 <= x<=5, as follows: For each n = 1,2,...,10, let h=10/n and y_n = P_n (1 + sqrt(10)), where P_n(x) is the interpolating polynomial for f(x) at the nodes (x_0)^(n), (x_1)^(n),..., (x_n)^(n) and (x_j)^(n) = 05 +j*h for each j = 0,1,2,...,n. Does the sequence {y_n} appear to converge on f(1 + sqrt(10))?

Help please 🙁

EDIT: This is in the section of the book after Langrange Polynomials and Neville's iteration so I assume we have to use that somehow.
EDIT v2.0: Scan of problem from book located at here

 

[Dufman]

id answer that question with True

🙂 sorry, i can be of no help

 

[StageLeft]

Originally posted by: amdmang
id answer that question with True

🙂 sorry, i can be of no help

 

[XZeroII]

Well, first we cry. Then we hide under the bed for awhile and hope that magically, everything works out fine.

 

[RaynorWolfcastle]

I might be able to figure out it meant if this was laid out in a more readable format (hint, hint)

 

[Kev]

Ha, child's play...I scoff at you for not being able to solve this in your head.

 

[Reel]

updated

 

[RaynorWolfcastle]

I've never covered this material, but this is what I'm assuming you have to do...

construct the polynomial as they describe... Sample the values for the polynomial at the appropriate points, then use some sort of mechanism to see if the polynomial gets closer to the original function as you add more terms.I imagine that using some graphing program to compare the poly's might help, otherwise you'll likely have to do some sort of error analysis to decide whether or not the sequence converges to your function with an increasing number of terms

Of course, I could be completely wrong since (like I said) I've never been taught this material.

Good luck 🙂

 

[Analog]

can't you do your own homework?

 

[Reel]

Originally posted by: RaynorWolfcastle
I've never covered this material, but this is what I'm assuming you have to do...

construct the polynomial as they describe... Sample the values for the polynomial at the appropriate points, then use some sort of mechanism to see if the polynomial gets closer to the original function as you add more terms.I imagine that using some graphing program to compare the poly's might help, otherwise you'll likely have to do some sort of error analysis to decide whether or not the sequence converges to your function with an increasing number of terms

Of course, I could be completely wrong since (like I said) I've never been taught this material.

Good luck 🙂

thanks. I was expecting something along those lines. I evaluated the Pn's and I am assuming I have to make a second interpolating polynomial that is composed of those Pn's. It does seem a bit confusing though and unfortunately the book has no examples along those lines. Everything up to this point has been generating a single interpolating polynomial.