Equation 2 · How Mathematics, Proof, and Scientific Computation Actually Work
What does this equation mean?
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the unit roundoff — roughly 10^{-16} for standard double precision — and is addition, subtraction, multiplication, or division. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol u
the unit roundoff — roughly 10^{-16} for standard double precision — and is addition, subtraction, multiplication, or division.
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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.) ↗
These citations give research context. Read each source to check which claims it supports.
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