Forward and backward error

  • Thread starter yenbibi
  • Start date
  • Tags
    Error
In summary, the conversation discusses the sine function given by an infinite series and the forward and backward errors that occur when approximating the function with only the first term or first two terms. The person is advised to show their work for assistance.
  • #1
yenbibi
2
0
The sine function is given by the infinite series
sin(x) = x - x3/3! + x5/5! + x7/7! + ...
a) What are the forward and backward errors if we approximate the sine function
by using only the first term in the series, for x = 0.1, 0.5, 1.0?
b) Using the first two terms.
 
Physics news on Phys.org
  • #2
Welcome to PF!

yenbibi said:
The sine function is given by the infinite series
sin(x) = x - x3/3! + x5/5! + x7/7! + ...
a) What are the forward and backward errors if we approximate the sine function
by using only the first term in the series, for x = 0.1, 0.5, 1.0?
b) Using the first two terms.

Hi yenbibi! Welcome to PF! :smile:

Show us what you've tried, and where you're stuck, and then we'll know how to help. :smile:
 
  • #3
Yes, show your work. Looks to me like a simple arithmetic problem.
 

What is the difference between forward and backward error?

The forward error of a numerical calculation is the difference between the exact solution and the approximate solution obtained. On the other hand, the backward error is the smallest perturbation in the input data that would result in the same approximate solution.

Why is it important to consider both forward and backward error?

Considering both forward and backward error allows us to assess the accuracy and stability of a numerical calculation. It gives us a better understanding of the limitations and potential errors in the results obtained.

How do you calculate forward and backward error?

To calculate the forward error, we can simply subtract the approximate solution from the exact solution. To calculate the backward error, we can use the condition number which measures how sensitive the solution is to small changes in the input data.

What is the relationship between forward and backward error?

The relationship between forward and backward error can be described as follows: if the forward error is small, then the backward error is also small. However, a small backward error does not guarantee a small forward error. This means that a small error in the input data may result in a larger error in the final solution.

How can forward and backward error be minimized?

To minimize forward and backward error, it is important to use efficient and accurate numerical algorithms and to carefully select the input data. Regularly checking and adjusting the precision of calculations can also help reduce error. Additionally, using error analysis techniques and considering the condition number can aid in minimizing errors in numerical calculations.

Similar threads

Iterative root finding for the cube root of 17
    • Precalculus Mathematics Homework Help
Replies
3
Views
3K
Can this be solved without trial and error?
    • Precalculus Mathematics Homework Help
Replies
6
Views
792
I Formula for the propagation of complex errors
    • General Math
Replies
5
Views
1K
Combining Sine Functions: Simplifying with Trigonometry
    • Precalculus Mathematics Homework Help
Replies
3
Views
1K
Trigonometric problem: Sin7x= Sin24 * 6.4
    • Introductory Physics Homework Help
Replies
12
Views
793
I Error bars in Excel (standard deviation, standard error, percentage)
    • Set Theory, Logic, Probability, Statistics
Replies
4
Views
921
Need help in manipulating rational absolute value inequalities
    • Precalculus Mathematics Homework Help
Replies
11
Views
1K
Thermal lattice Boltzmann model ignoring source term -- python code help please
    • Programming and Computer Science
Replies
1
Views
1K
Finding an angle of a triangle as function of another angle
    • Precalculus Mathematics Homework Help
Replies
21
Views
3K
I Error Propagation in Measurements
    • General Math
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top