About: Kahan summation algorithm

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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 obvious approach. This is done by keeping a separate running compensation (a variable to accumulate small errors), in effect extending the precision of the sum by the precision of the compensation variable.

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rdfs:label	Kahan summation algorithm (en)
rdfs:comment	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 obvious approach. This is done by keeping a separate running compensation (a variable to accumulate small errors), in effect extending the precision of the sum by the precision of the compensation variable. (en)
sameAs	Kahan summation algorithm
dbp:wikiPageUsesTemplate	dbt:Citation_needed dbt:Reflist dbt:Confusing
Subject	Articles with example pseudocode Computer arithmetic Numerical analysis
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Kahan_summation_algorithm?oldid=1070449205&ns=0
Wikipage page ID	373216 (xsd:integer)
page length (characters) of wiki page	26286 (xsd:nonNegativeInteger)
Wikipage revision ID	1070449205 (xsd:integer)
Link from a Wikipage to another Wikipage	Floating-point arithmetic Fortran Machine epsilon Numerical analysis Numerical error Numerical stability Root mean square William Kahan 2Sum ANSI C Algorithm Algorithms for calculating variance Amortization Approximation error Arbitrary-precision arithmetic Associative property Basic Linear Algebra Subprograms Sequence Volatile (computer programming) Bresenham's line algorithm C (programming language) C Sharp (programming language) Articles with example pseudocode Computer arithmetic Jonathan Shewchuk Julia (programming language) Numerical analysis Double-precision floating-point format Pairwise summation Python (programming language) Quadruple-precision floating-point format Delta-sigma modulation Linear algebra Pseudocode Condition number Optimizing compiler Fast Fourier transform Intel C++ Compiler Ivo Babuška Random walk Recursion Sign (mathematics) Significant figures Single instruction, multiple data Ulrich Kulisch
has abstract	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 obvious approach. This is done by keeping a separate running compensation (a variable to accumulate small errors), in effect extending the precision of the sum by the precision of the compensation variable. In particular, simply summing numbers in sequence has a worst-case error that grows proportional to , and a root mean square error that grows as for random inputs (the roundoff errors form a random walk). With compensated summation, using a compensation variable with sufficiently high precision the worst-case error bound is effectively independent of , so a large number of values can be summed with an error that only depends on the floating-point precision of the result. The algorithm is attributed to William Kahan; Ivo Babuška seems to have come up with a similar algorithm independently (hence Kahan–Babuška summation). Similar, earlier techniques are, for example, Bresenham's line algorithm, keeping track of the accumulated error in integer operations (although first documented around the same time) and the delta-sigma modulation. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Kahan_summation_algorithm
is Wikipage redirect of	Kahan Summation Algorithm Kahan sum Kahan summation Compensated summation
is Link from a Wikipage to another Wikipage of	Floating-point arithmetic Numerical error 2Sum Algorithms for calculating variance Associative property Kahan (disambiguation) Kahan Summation Algorithm Dot product Decimal floating point List of numerical analysis topics List of University of Toronto alumni List of algorithms Euler method Kahan sum Kahan summation Ivo Babuška Loss of significance Compensated summation
is known for of	William Kahan
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Kahan_summation_algorithm

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