Relative error

Definition

Relative error measures the accuracy of an approximation by comparing the absolute error to the exact value. It is often expressed as a percentage.

5 Must Know Facts For Your Next Test

1. Relative error is given by the formula: $\text{Relative Error} = \frac{\text{Absolute Error}}{\text{Exact Value}}$.
2. In numerical integration, relative error helps assess how close an estimated integral is to the actual integral value.
3. A smaller relative error indicates a more accurate approximation.
4. Relative error can be particularly important when dealing with very large or very small integral values.
5. It is dimensionless and often expressed as a percentage by multiplying by 100.

Review Questions

• What is the formula for calculating relative error?
• Why is relative error important in numerical integration?
• How do you express relative error as a percentage?

Related terms

Absolute Error: The difference between the exact value and the approximated value.

Numerical Integration: A set of algorithms for approximating the value of definite integrals.

Trapezoidal Rule: A numerical method to approximate definite integrals by summing up areas of trapezoids under a curve.