Computing true percent relative error (Taylor Series)

Thread starter jegues
Start date Jan 14, 2011
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Computing Error Percent Relative Series Taylor series

In summary, computing true percent relative error is a method used to measure the accuracy of a mathematical approximation or calculation. It takes into account the magnitude of the true value and is more accurate for larger values compared to absolute error. The Taylor Series is commonly used for this calculation as it provides a more accurate representation of the true value. However, there are limitations to this method, such as assuming the approximate value is close to the true value and not accounting for systematic errors. In scientific research, computing true percent relative error is helpful in determining the accuracy and reliability of calculations, and can guide further experimentation or improvements.

Jan 14, 2011

jegues

Homework Statement

See figure attached,

attachment.php?attachmentid=31324&stc=1&d=1295049772.jpg

Homework Equations

The Attempt at a Solution

Isn't the Maclaurin series just simply the Taylor series around 0?

[tex](\text{i.e. } (x-c), \quad c=0, \quad x )[/tex]

Also for part B, how do we go about solving for [tex]| \epsilon_{t} |[/tex]?

Thanks again!

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Jan 15, 2011

jegues

Bump, still looking for some help

FAQ: Computing true percent relative error (Taylor Series)

1. What is computing true percent relative error?

Computing true percent relative error is a method used to measure the accuracy of a mathematical approximation or calculation. It is calculated by taking the absolute difference between the true value and the approximate value, dividing it by the true value, and multiplying by 100 to get a percentage.

2. How is computing true percent relative error different from absolute error?

Absolute error measures the difference between the true value and the approximate value, while computing true percent relative error takes into account the magnitude of the true value. This means that computing true percent relative error is a more accurate measure of error for larger values.

3. Why is the Taylor Series used for computing true percent relative error?

The Taylor Series is used because it provides a way to approximate a function with a polynomial, making it easier to calculate the error. Additionally, the Taylor Series is a more accurate representation of the true value compared to other methods.

4. What are the limitations of computing true percent relative error?

Computing true percent relative error assumes that the approximate value is close to the true value, and it does not take into account any systematic errors in the calculation. Additionally, it may not be suitable for all types of functions and may require a higher degree polynomial approximation for more accurate results.

5. How can computing true percent relative error be useful in scientific research?

Computing true percent relative error is important in scientific research as it allows researchers to determine the accuracy and reliability of their calculations. It can also help identify areas where the calculation may need to be improved or where further experimentation is needed.