Karlsruhe Accurate Arithmetic (KAA) or Karlsruhe Accurate Arithmetic Approach (KAAA), augments conventional
floating-point arithmetic with good error behaviour with new operations to calculate
scalar product
In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an alge ...
s with a single rounding error.
The foundations for KAA were developed at the
University of Karlsruhe
The Karlsruhe Institute of Technology (KIT; german: Karlsruher Institut für Technologie) is a public research university in Karlsruhe, Germany. The institute is a national research center of the Helmholtz Association.
KIT was created in 2009 w ...
starting in the late 1960s.
See also
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Ulrich W. Kulisch
Ulrich W. Kulisch (born 1933 in Breslau) is a German mathematician specializing in numerical analysis, including the computer implementation of interval arithmetic.
Experience
After graduation from high school in Freising, Kulisch studied mathe ...
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IBM 4361
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PCS Cadmus
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FORTRAN-SC
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PASCAL-SC
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PASCAL-XSC
Pascal is an Imperative programming, imperative and Procedural programming, procedural programming language, designed by Niklaus Wirth as a small, efficient language intended to encourage good programming practices using structured programming an ...
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C-XSC
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Extensions for Scientific Computation
Interval arithmetic (also known as interval mathematics, interval analysis, or interval computation) is a mathematical technique used to put bounds on rounding errors and measurement errors in mathematical computation. Numerical methods using ...
(XSC)
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Triplex-ALGOL Karlsruhe
ALGOL (; short for "Algorithmic Language") is a family of imperative computer programming languages originally developed in 1958. ALGOL heavily influenced many other languages and was the standard method for algorithm description used by the ...
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Interval arithmetic
Interval arithmetic (also known as interval mathematics, interval analysis, or interval computation) is a mathematical technique used to put bounds on rounding errors and measurement errors in mathematical computation. Numerical methods usin ...
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Unum
Unum Group is an American insurance company headquartered in Chattanooga, Tennessee. Founded as Union Mutual in 1848 and known as UnumProvident from 1999-2007, the company is part of the Fortune 500. Unum Group was created by the 1999 merger of ...
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Catastrophic cancellation
References
Further reading
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* {{cite journal , title=Numerische Mathematik: Rechnen mit garantierter Genauigkeit , trans-title=Numerical mathematics: Calculating with guaranteed accuracy , author-first=Christoph , author-last=Pöppe , journal=
Spektrum der Wissenschaft
''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it i ...
, language=German , number=9 , volume=2000 , date=2000-09-01 , pages=54– , publisher=
Spektrum der Wissenschaft Verlagsgesellschaft mbH , url=http://www.spektrum.de/magazin/rechnen-mit-garantierter-genauigkeit/826769 , access-date=2016-05-30 , url-status=live , archive-url=https://web.archive.org/web/20160530222045/http://www.spektrum.de/magazin/rechnen-mit-garantierter-genauigkeit/826769 , archive-date=2016-05-30
Computer arithmetic
Numerical analysis