Simpson's Rule with negative values

  • Context: Undergrad 
  • Thread starter Thread starter amanno
  • Start date Start date
  • Tags Tags
    Negative
Click For Summary
SUMMARY

This discussion focuses on the application of Simpson's Rule in digital integration, specifically addressing the impact of negative values on the accuracy of the integral approximation. It is established that the presence of negative function values does not affect the accuracy of Simpson's Rule. Users can add a fixed constant to each sample value without compromising the integrity of the results, as this adjustment merely shifts the integral without altering its accuracy.

PREREQUISITES
  • Understanding of Simpson's Rule for numerical integration
  • Basic knowledge of digital signal processing
  • Familiarity with sampling techniques and their implications
  • Concept of integral approximation in numerical methods
NEXT STEPS
  • Explore the mathematical foundations of Simpson's Rule
  • Research the effects of sampling frequency on numerical integration accuracy
  • Learn about error analysis in numerical methods
  • Investigate alternative numerical integration techniques such as Trapezoidal Rule
USEFUL FOR

Mathematicians, engineers, and data scientists involved in numerical methods, digital signal processing, and anyone seeking to enhance their understanding of integration techniques with real-world applications.

amanno
Messages
22
Reaction score
0
Hey guys,

Not claiming to be an expert on numerical methods here but I am doing some digital integration using simpson's rule that takes 10 samples a second to provide me with the "approximate" integral for that time period.

Right now I am currently taking the magnitude of the value I receive (before integrating it), it is possible that for some of my samples, within the 1 second time period, could be negative. What does this do to the result of simpsons rule? Will it still provide accurate results or is the error greater?

Thanks!
 
Physics news on Phys.org
Whether or not there are negative function values does not change the accuracy of Simpson's. You can, in fact, add a fixed number to each value- adding that number times the length of the interval to the integral but not changing the accuracy.
 

Similar threads

MHB Calculating Integral with Simpson's Rule for Error < $0.5\cdot 10^{-3}$
  • · Replies 6 ·
Replies
6
Views
2K
MHB Trapezoid & Simpson's Rule with their respective errors.
  • · Replies 2 ·
Replies
2
Views
2K
Estimating Error w/ Trap and Simpson's Rule when Values are Equal
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Numerical Integration twice (acceleration to displacement)
  • · Replies 5 ·
Replies
5
Views
5K
MHB Applying Simpson's Rule with 7 Pieces: Solving the Int.
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad How Can Simpson's Rule Be Adjusted for Functions Undefined at Boundary Points?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Finding the Largest (or smallest) Value of a Function - given some constant symmetric errors
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Taming a Divergent Series -- But how does it work?
  • · Replies 14 ·
Replies
14
Views
3K
Undergrad Error propagation of a variable for an integral
  • · Replies 6 ·
Replies
6
Views
5K
Graduate Approximating f(x) with Midpoint, Trapezoidal & Simpson's Rule
  • · Replies 1 ·
Replies
1
Views
6K