Karlsruhe Accurate Arithmetic (KAA) or Karlsruhe Accurate Arithmetic Approach (KAAA), augments conventional
floating-point arithmetic
In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be ...
with good error behaviour with new operations to calculate
scalar products 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
The IBM 4300 series are mid-range systems compatible with System/370 that were sold from 1979 through 1992. They featured modest electrical and cooling requirements, and thus did not require a data center environment. They had a disruptive effect ...
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PCS Cadmus
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FORTRAN-SC
Interval arithmetic (also known as interval mathematics, interval analysis, or interval computation) is a mathematical technique used to Floating point error mitigation, put bounds on rounding errors and measurement errors in numerical analysis ...
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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
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 usi ...
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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 using ...
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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
In numerical analysis, catastrophic cancellation is the phenomenon that subtracting good approximations to two nearby numbers may yield a very bad approximation to the difference of the original numbers.
For example, if there are two studs, one L_ ...
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 , language=German , number=9 , volume=2000 , date=2000-09-01 , pages=54– , publisher=
Spektrum der Wissenschaft Verlagsgesellschaft mbH
''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 ...
, 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