Truncation Error

Numerical Analysis · Axiom Academy

The error from approximating infinite processes with finite ones The Taylor series for e^x has infinitely many terms. We must stop somewhere—the discarded terms are the truncation error. Numerical derivatives use finite differences instead of limits. The step size h controls the truncation error. We describe truncation error by its order : O(h), O(h²), etc. Higher order means faster error decrease as h shrinks. 4. Truncation vs Round-off Trade-off As step size decreases, truncation error falls but round-off error rises. The optimal choice balances both.

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