Numerical Methods: 3 Point Formula

In summary, the conversation discussed an example in a Numerical Methods course where the 3-point formula was used to approximate the first derivative of f. The example included 4 given x's and their corresponding images by f. The first 3 x's were used to calculate f' using one of the two 3-point formulas, but the 4th x was left without an attempt to find its f'(x). The question asked was whether there is a solution to this and if it is possible to use a negative h to estimate f' for the 4th point.
  • #1
bobmerhebi
38
0
Hello there,

I am taking a Numerical Methods course & i had a lecture today when we did an example on the 3-point formula to approximate the 1st derivative of f.

the example included 4 given x's with their images by f. & we had to get all the images for the 1st derivative of f.

so we used one of the two 3-point formulas to get the values for f' for each of the first 3 x's. the last x was left without an attempt to get its f'(x).

So tonight i was wondering about how could I apply the formula to get it & its seems that I can't, after all either of the 3 point formula's requires the values of either the previous & following x or the two values following x. In either cases that's not possible as there's is no value after this particular x.

my question is whether there's some kind of solution to this & if so or not how so ?

P.S. this is Not a HW question but rather a help in my lecture.

Thank you
 
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  • #2
To estimate f' for the 4th point, can't you use the same method as the 1st point? In other words, can't h be negative?
 

FAQ: Numerical Methods: 3 Point Formula

What is the 3 point formula in numerical methods?

The 3 point formula in numerical methods is a mathematical technique used to approximate the value of a function at a given point using the values of the function at three nearby points. It is often used in numerical integration and differentiation.

How does the 3 point formula work?

The 3 point formula uses the values of the function at three points (x-h, x, x+h) to approximate the value of the function at a point x. It uses a weighted average of the function values at these points to calculate the approximation.

What are the advantages of using the 3 point formula?

One advantage of using the 3 point formula is that it is relatively simple to implement and can provide a good approximation of the function value. It also allows for a smaller step size compared to other numerical methods, which can result in a more accurate approximation.

What are the limitations of the 3 point formula?

One limitation of the 3 point formula is that it is only accurate for functions that are smooth and continuous. It also requires the calculation of multiple function values, which can be time-consuming for complex functions.

How can the accuracy of the 3 point formula be improved?

The accuracy of the 3 point formula can be improved by using a smaller step size, which means calculating the function values at more points. It can also be improved by using a higher-order formula, such as the 5 point formula, which uses more points and provides a more accurate approximation.

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