Interpolation using divided differences

In summary, the conversation is about deriving an interpolation polynomial using divided differences from a given set of data points. One person is confused about how to do this without knowing the function, while the other clarifies that they only need to know the value of the function at known points to calculate the divided differences and construct the interpolant polynomial.
  • #1
ACLerok
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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.
 
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  • #2
One of us is very confused on this! The problem says "using divided differences". Are you saying you do not know what that is?
 
  • #3
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.
 
  • #4
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).
 

FAQ: Interpolation using divided differences

What is interpolation using divided differences?

Interpolation using divided differences is a mathematical method for approximating a function using a finite set of data points. It involves finding a polynomial that passes through the given data points and can be used to estimate the value of the function at other points within the range.

How is interpolation using divided differences different from other interpolation methods?

Unlike other interpolation methods that use a single polynomial to approximate the function, interpolation using divided differences uses a piecewise polynomial that passes through each data point. This results in a more accurate estimation of the function.

What is the purpose of using divided differences in interpolation?

The use of divided differences in interpolation helps to simplify the process of finding the polynomial that passes through the given data points. It also allows for the easy evaluation of the function at any point within the range without having to go through the entire process again.

What are the limitations of interpolation using divided differences?

One limitation of this method is that it can only be used for evenly spaced data points. It also does not take into account any external factors that may affect the behavior of the function, such as outliers or noise in the data.

In what fields is interpolation using divided differences commonly used?

This method is commonly used in fields such as engineering, physics, and computer science for data analysis and forecasting. It is also used in numerical analysis for solving problems involving differential equations.

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