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Numerical Error

High School

Definition

Numerical error arises in computer calculations. Types include rounding error, truncation error, and propagation error.

Absolute error = |x - \tildex|

Absolute error

Relative error = \frac|x - \tildex||x|

Relative error

ε_machine ≈ 2.2 × 10^-16

Double precision machine epsilon

Example 1

If true value is π and approximation is 3.14, find relative error.

Calculation reliability

Precision calculations

Simulation accuracy