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 b ...
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 alg ...
s with a single rounding error.
The foundations for KAA were developed at the
University of Karlsruhe starting in the late 1960s.
See also
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Ulrich W. Kulisch
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IBM 4361
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PCS Cadmus
Periphere Computer Systeme (PCS) was founded in Munich by the brothers Georg and Eberhard Färber in 1969. In the 1980s and 1990s it was a manufacturer of a line of UNIX-based workstations called "". Their flavor of System V was called ; it w ...
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FORTRAN-SC
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 us ...
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PASCAL-SC
Pascal is an imperative and procedural programming language, designed by Niklaus Wirth as a small, efficient language intended to encourage good programming practices using structured programming and data structuring. It is named in honour of ...
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PASCAL-XSC
Pascal is an imperative and procedural programming language, designed by Niklaus Wirth as a small, efficient language intended to encourage good programming practices using structured programming and data structuring. It is named in honour of ...
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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 (XSC)
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Triplex-ALGOL Karlsruhe
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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
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