Simpson's Rule with negative values

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In summary, the speaker is using Simpson's rule to perform digital integration, with 10 samples per second, to get an approximate integral for a 1 second time period. They are wondering if negative function values will affect the accuracy of the results. They are informed that adding a fixed number to each value will not change the accuracy of Simpson's rule.
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amanno
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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!
 
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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.
 

What is Simpson's Rule with negative values?

Simpson's Rule is a numerical integration method used to approximate the area under a curve. It can also be used to approximate definite integrals with negative values.

How does Simpson's Rule with negative values work?

Simpson's Rule with negative values works by dividing the area under the curve into smaller sections, approximating each section with a parabola, and then summing up the areas of all the parabolas to get an overall approximation of the area under the curve.

Can Simpson's Rule with negative values be used for any type of curve?

Yes, Simpson's Rule with negative values can be used for any type of curve, as long as the curve can be approximated by a series of parabolas.

Are there any limitations to using Simpson's Rule with negative values?

One limitation of Simpson's Rule with negative values is that it may not provide an accurate approximation for curves with sharp turns or discontinuities. It also requires an even number of intervals to work properly.

When should Simpson's Rule with negative values be used instead of other numerical integration methods?

Simpson's Rule with negative values should be used when the curve being integrated has negative values and when a higher degree of accuracy is desired compared to other numerical integration methods such as the Trapezoidal Rule. It is also more efficient when the number of intervals is relatively large.

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