Interpolation using divided differences

  • Thread starter Thread starter ACLerok
  • Start date Start date
  • Tags Tags
    Interpolation
Click For Summary

Homework Help Overview

The discussion revolves around deriving an interpolation polynomial using divided differences based on a set of data points. The original poster expresses confusion regarding the absence of a specific function f(x) and questions how to proceed with the interpolation without it.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the necessity of knowing f(x) for calculating divided differences and whether it is acceptable to infer a function from plotted data points. There is a discussion about the distinction between needing f(x) and needing the interpolating polynomial P(x).

Discussion Status

The conversation is ongoing, with some participants clarifying that while f(x) is not provided, the values at known points can be used to construct the interpolating polynomial. There is no explicit consensus yet, as confusion remains about the requirements for the interpolation process.

Contextual Notes

Participants are grappling with the implications of the problem statement, particularly regarding the assumptions about the function f(x) and the data points provided.

ACLerok
Messages
194
Reaction score
0

Homework Statement


Given a set of data points, derive the interpolation polynomial using divided differences.


Homework Equations





The Attempt at a Solution


My main question is: How am I supposed to do this if they don't give f(x)? Can I just look at the plotted data points and 'guess' the function (cos,sin,tan) that will best fit them? As a test, I tried using f(x)=cosx and graphed the resulting equation but it did not meet at the given points.
 
Physics news on Phys.org
One of us is very confused on this! The problem says "using divided differences". Are you saying you do not know what that is?
 
I know what it is. I'm saying that I am supposed to find the interpolation formula but they don't say what f(x). You need f(x) to calculate the divided differences.
 
No, you don't need to know f(x) but P(x) which is the interpolant polynome. They don't give f(x) but they give the value of f(x) at known points. From this, you can do the divided differences and build the P(x). All this without knowing f(x).
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 1 ·
Replies
1
Views
12K