Everything about Round-off error
Computational error due to rounding numbers
In computing, a roundoff error, also called rounding error, is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. Rounding errors are due to inexactness in the representation of real numbers and the arithmetic operations done with them. This is a form of quantization error. When using approximation equations or algorithms, especially when using finitely many digits to represent real numbers, one of the goals of numerical analysis is to estimate computation errors. Computation errors, also called numerical errors, include both truncation errors and roundoff errors. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Round-off errorA 5-minute orientation
- Skim a recent paper: A novel feed rate scheduling method with acc-jerk-continuity and round-off error elimination for non-uniform rational B-spline interpolationInfluential work since 2022
- Pick up a classic book: Winsor McCayThe most-reprinted book on the subject
- Read the landmark paper: CADNA: a library for estimating round-off error propagationCited 83 times
- Go sideways: Machine epsilonA closely related topic
- Go sideways: Floating-point arithmeticA closely related topic
📖 Definitions
Noun The difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic.
🏆 Landmark papers (most cited)
CADNA: a library for estimating round-off error propagation
Round-off error propagation in four generally-applicable, recursive, least-squares estimation schemes
Accumulation of Round-Off Error in Fast Fourier Transforms
Complexity estimates depending on condition and round-off error
Integrated volatility and round-off error
Parameter Optimization and Reduction of Round Off Error for the Gegenbauer Reconstruction Method
Backward consistency concept and round-off error propagation dynamics in recursive least-squares algorithms
Review on stochastic approach to round-off error analysis and its applications
🆕 Influential since 2022
A novel feed rate scheduling method with acc-jerk-continuity and round-off error elimination for non-uniform rational B-spline interpolation
Parallel Algorithm for Solving Overdetermined Systems of Linear Equations, Taking into Account Round-Off Errors
Round-Off Error Analysis in mMIMO Detector Based on Cholesky Decomposition
Accounting for Round-Off Errors When Using Gradient Minimization Methods
Avoiding round-off error in the Rachford–Rice equation
📚 Books worth reading
Winsor McCayWinsor McCay · 2003
The Conspirators HierarchyJohn Coleman · 1992
Treaty Occupationay ToxicologySuelen Queiroz · 2010
Direction and position finding by wirelessRonald Keen · 1920
The creed explainedDevine, Arthur · 1897- 📕On round-off errors in linear programmingHeiner Müller-Merbach · 1970
- 📕Round-off error propogation in four generally applicable, recursive, least-squares-estimation schemesM. H. Verhaegen · 1988
The little flowers of the glorious Messer St. Francis and of his friarsFrancis of Assisi, Heywood, William, 1857-1919 · 1906
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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