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Everything about Kahan summation algorithm
Algorithm in numerical analysis
In numerical analysis, the Kahan summation algorithm, also known as compensated summation, significantly reduces the numerical error in the total obtained by adding a sequence of finite-precision floating-point numbers, compared to the naive approach. This is done by keeping a separate running compensation, in effect extending the precision of the sum by the precision of the compensation variable. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Kahan summation algorithmA 5-minute orientation
- Skim a recent paper: Error-Summation Enhanced Newton Algorithm for Model Predictive Control of Redundant ManipulatorsInfluential work since 2022
- Pick up a classic book: Numerical Algorithms for Number TheoryThe most-reprinted book on the subject
- Read the landmark paper: A Distillation Algorithm for Floating-Point SummationCited 21 times
- Go sideways: Pairwise summationA closely related topic
- Go sideways: Summation algorithmA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
A Distillation Algorithm for Floating-Point Summation
A self-cited pixel summation based image encryption algorithm*
A New Distillation Algorithm for Floating-Point Summation
A Generalized Kahan-Babuška-Summation-Algorithm
An adaptable summation algorithm
A new error-free floating-point summation algorithm
Auto Focusing Algorithm Based on Largest Gray Gradient Summation
A novel algorithm for nested summation and hypergeometric expansions
🆕 Influential since 2022
Error-Summation Enhanced Newton Algorithm for Model Predictive Control of Redundant Manipulators
Multi-level parallel multi-layer block reproducible summation algorithm
A fast parallel high-precision summation algorithm based on AccSumK
Simultaneous multi-controller fusion via genetic algorithm-optimized weighted summation for variable-speed wind turbine control
Horizontal well placement optimization based on matrix directional continuous element summation algorithm
📚 Books worth reading
Numerical Algorithms for Number TheoryKarim Belabas, Henri Cohen · 2021
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Pairwise summation In numerical analysis, pairwise summation, also called cascade summation, is a summation algorithm, i.e. a technique to sum a sequence of finite-precision…
- Summation algorithm A summation algorithm is an algorithm that computes the sum of a finite list of numbers ∑L[i]. It is especially relevant in floating-point arithmetic where…
- 2Sum 2Sum is a floating-point algorithm for computing the exact round-off error in a floating-point addition operation. 2Sum and its variant Fast2Sum were first…
- Machine epsilon Machine epsilon or machine precision is an upper bound on the relative approximation error due to rounding in floating point number systems. This value…
- Studentized residual In statistics, a studentized residual is the dimensionless ratio resulting from the division of a residual by an estimate of its standard deviation, both…
- Catastrophic cancellation In numerical analysis, catastrophic cancellation is the phenomenon that subtracting good approximations to two nearby numbers may yield a very bad approximation…
- Round-off error In computing, a roundoff error, also called rounding error, is the difference between the result produced by a given algorithm using exact arithmetic and…
- Approximation theory In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing…