How Accurate is Lagrange Interpolation for Approximating Cos(0.75)?

In summary: I understand your concern, but I don't want to risk any accusations of plagiarism. Thank you for understanding.I will post it after the course is over. I understand your concern, but I don't want to risk any accusations of plagiarism. Thank you for understanding.In summary, the problem involves using the Lagrange interpolating polynomial of degree three or less and four digit chopping arithmetic to approximate cos(.750) with four given values. The solution provides an approximation of cos(.7500), the actual error and an error bound for the approximation. The discrepancy between the actual error and the error bound is due to the given data being limited to only four decimal places. The individual seeking help solved the problem themselves but was disappointed
  • #1
Hero1
9
0
Problem:
Use the Lagrange interpolating polynomial of degree three or less and four digit chopping arithmetic to approximate cos(.750) using the following values. Find an error bound for the approximation.

cos(.6980) = 0.7661
cos(.7330) = 0.7432
cos(.7680) = 0.7193
cos(.8030) = 0.6946

The actual value of cos(.7500) = 0.7317 (to four decimal places). Explain the discrepancy between the actual error and the error bound.

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Solution:
The approximation of cos(.7500) 0.7313. The actual error is 0.0004, and an error bound is 2.7 × 10-8. The discrepancy is due to the fact that the data are given only to four decimal places.

_________________________________________________________________________________________________

Can anyone help me figure out the intermediary steps from the problem to solution?
 
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  • #2
I managed to figure out the solution to the problem myself, however, I am disappointed that no one responded to my thread.
 
  • #3
Hero said:
I managed to figure out the solution to the problem myself, however, I am disappointed that no one responded to my thread.

Hi Hero,

I'm sorry no one responded to your thread. Over 95% of our threads get responded to, so believe me it's not a normal occurrence. Can you post how you solved the problem for us? Other people in the future might find it useful :)

Jameson
 
  • #4
Jameson said:
Hi Hero,

I'm sorry no one responded to your thread. Over 95% of our threads get responded to, so believe me it's not a normal occurrence. Can you post how you solved the problem for us? Other people in the future might find it useful :)

Jameson

I can't post it until after the course is over. I don't want my instructor thinking that I stole online content.
 
  • #5
Hero said:
I can't post it until after the course is over. I don't want my instructor thinking that I stole online content.

You posted the question here hoping someone else would answer it. How is your posting your own work different than someone else posting their work?

I guess if you just won't post your solution, then ok but I don't quite get it. As a rule of thumb I would suggest that you be comfortable with anything you post on this site to be read by anyone.

Again, sorry you didn't get any help but give it one more try and when another question comes up and I'm sure you'll find some help. I'll make sure our staff knows that you have a question if you post next time.
 
  • #6
Jameson said:
You posted the question here hoping someone else would answer it. How is your posting your own work different than someone else posting their work?

I guess if you just won't post your solution, then ok but I don't quite get it. As a rule of thumb I would suggest that you be comfortable with anything you post on this site to be read by anyone.

Again, sorry you didn't get any help but give it one more try and when another question comes up and I'm sure you'll find some help. I'll make sure our staff knows that you have a question if you post next time.

I will post it
 

FAQ: How Accurate is Lagrange Interpolation for Approximating Cos(0.75)?

What is interpolation and how is it used in science?

Interpolation is a mathematical method used to estimate the value of a function or data point within a given set of known points. In science, interpolation is commonly used to fill in missing data points or to make predictions based on existing data.

What is the purpose of calculating error bound in interpolation?

The error bound in interpolation is an important measure of the accuracy of the estimated values. It gives an upper limit on the difference between the estimated value and the actual value, and helps to determine how reliable the interpolation results are.

How is error bound calculated in interpolation?

Error bound is calculated using a formula that takes into account the number of known data points, the distance between those points, and the degree of the interpolating polynomial. This formula allows for a more accurate estimation of the error compared to simply looking at the difference between the estimated and actual values.

Can interpolation always provide an exact representation of the original data?

No, interpolation is an approximation method and can only provide an exact representation of the original data if the function being interpolated is a polynomial and the data points are exact. In most real-world scenarios, interpolation can only provide an estimation of the original data.

What are some potential sources of error in interpolation?

Some potential sources of error in interpolation include rounding errors, limitations of the interpolation method used, and the presence of outliers or irregularities in the data. It is important to carefully consider these sources of error and their potential impact on the accuracy of the interpolation results.

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