University · Mathematics · Numerical Analysis
Error Analysis and Floating-Point Arithmetic
Every numerical method studied in this unit — bisection, Newton's method, quadrature, interpolation — is eventually executed in finite-precision floating-point arithmetic, which introduces its own error on top of the method's mathematical approximation error. This topic distinguishes truncation error from round-off error, explains IEEE 754 floating-point representation and machine epsilon, and demonstrates catastrophic cancellation, a real and dangerous phenomenon that can silently destroy the a
Inhaltsübersicht
- Two Sources of Error: Truncation and Round-off
- Floating-Point Representation and Machine Epsilon
- Catastrophic Cancellation: When Subtraction Destroys Precision
- Avoiding Cancellation in Practice, and Its Connection to This Unit's Other Methods
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