Newton interpolary difference formula

In summary, the conversation is about understanding the meaning of a formula and its variables, specifically f(x1, x2) and f(x0, x1). The formula is used to find the second divided difference and the participant's attempt resulted in a value of -0.143. The conversation ends with a reminder not to post images and to type out the work instead.
  • #1
fonseh
529
2

Homework Statement


I don't understand the meaning of the formula... For the circled part in the first photo , what is the meaning of f(x1 ,x2 ) ? and also f(x0 , x1 ) ?

Homework Equations

The Attempt at a Solution


I used the highlighted formula to find the second divided difference . But , Here's what i gt :

f(x1 ,x2 ) - f(x0 , x1 ) / ( x2 -x0 )
=
(0.510*0.381)-(0.521*0.510) / (2.6-2.1) , I ended up getting -0.143
 

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  • #2
fonseh said:

Homework Statement


I don't understand the meaning of the formula... For the circled part in the first photo , what is the meaning of f(x1 ,x2 ) ? and also f(x0 , x1 ) ?

Homework Equations

The Attempt at a Solution


I used the highlighted formula to find the second divided difference . But , Here's what i gt :
(0.510*0.381)-(0.521*0.510) / (2.6-2.1) , I ended up getting -0.143

Do not post images; type out your work.
 
  • Like
Likes fonseh
  • #3
Ray Vickson said:
Do not post images; type out your work.
It's just the notes ... For my trial , i didnt post images ...
 

FAQ: Newton interpolary difference formula

What is Newton interpolary difference formula?

The Newton interpolary difference formula is a mathematical method used to approximate the value of a function at a point within a given range of values. It is based on the concept of divided differences, which is used to simplify the process of calculating higher-order derivatives of a function.

How does the Newton interpolary difference formula work?

The formula uses a set of data points to construct a polynomial function that passes through those points. This polynomial function is then used to estimate the value of the function at any point within the given range by using the values of the function at the data points.

What are the advantages of using the Newton interpolary difference formula?

One advantage is that it is a relatively simple and efficient method for approximating the value of a function. It also allows for more accurate estimation compared to other interpolation methods, especially when the data points are evenly spaced.

What are the limitations of the Newton interpolary difference formula?

One limitation is that the accuracy of the approximation decreases as the distance between data points increases. This means that the formula may not be as effective for non-uniformly distributed data. Additionally, the use of higher-order polynomials can lead to numerical instability and errors.

In what fields is the Newton interpolary difference formula commonly used?

The formula is commonly used in fields such as mathematics, engineering, and computer science for tasks such as curve fitting, function approximation, and solving differential equations. It can also be applied in various scientific and technological applications that require data analysis and prediction.

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