Equation 3 · How Mathematics, Proof, and Scientific Computation Actually Work
What does this equation mean?
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superscript
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
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What the article says around this equation
where u is the unit roundoff — roughly 10^{-16} for standard double precision — and is addition, subtraction, multiplication, or division. Each single step, in other words, is correct up to a tiny, precisely bounded relative error.
Sources cited in the article section
- [5] IEEE 754-2019 — IEEE Standard for Floating-Point Arithmetic ↗
- [6] Accuracy and Stability of Numerical Algorithms (2nd ed.) ↗
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