Error Analysis

Error analysis quantifies inaccuracies in numerical methods, ensuring reliable computational results.

Types of Errors

Truncation error (approximation) and round-off error (finite precision) are key: \(E = |x_{\text{exact}} - x_{\text{approx}}|\).

Examples

Adding 0.1 ten times in floating-point may yield 0.999... due to round-off, not 1.

Error Control

Smaller step sizes reduce truncation error; higher precision mitigates round-off.