Absolute error

Definition

Absolute error is the difference between the exact value of an integral and its numerical approximation. It quantifies the magnitude of error without considering its direction.

5 Must Know Facts For Your Next Test

1. The formula for absolute error is $|I - A|$, where $I$ is the exact value and $A$ is the approximate value.
2. Absolute error is always a non-negative number.
3. In numerical integration, minimizing absolute error improves the accuracy of approximations like the Trapezoidal Rule or Simpson's Rule.
4. Absolute error can be reduced by increasing the number of intervals (subdivisions) in numerical methods.
5. It provides a straightforward measure to compare different numerical methods' precision.

Review Questions

• What does absolute error measure in numerical integration?
• How do you calculate absolute error for an integral approximation?
• Why is it important to minimize absolute error in numerical integration?

Related terms

Relative Error: The ratio of the absolute error to the exact value, often expressed as a percentage.

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

Simpson's Rule: A method for numerical integration that approximates the integral by using parabolic arcs instead of line segments.