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ACRITH-XSC

swMATH ID: 15
Software Authors: Walter, Wolfgang V.
Description: ACRITH-XSC is a Fortran-like programming language designed for the development of self-validating numerical algorithms. Such algorithms deliver results of high accuracy which are verified to be correct by the computer. Thus there is no need to perform an error analysis by hand for these calculations. For example, self-validating numerical techniques have been successfully applied to a variety of engineering problems in soil mechanics, optics of liquid crystals, ground-water modelling and vibrational mechanics where conventional floating-point methods have failed.
With few exceptions, ACRITH-XSC is an extension of FORTRAN 77. Various language concepts which are available in a ACRITH-XSC can also be found in a more or less similar form in Fortran 90. Other ACRITH-XSC features have been specifically designed for numerical purposes: numeric constant and data conversion and arithmetic operators with rounding control, interval and complex interval arithmetic, accurate vector/matrix arithmetic, an enlarged set of mathematical standard functions for point and interval arguments, and more. For a restricted class of expressions called “dot product expressions”, ACRITH-XSC provides a special notation which guarantees that expressions of this type are evaluated with least-bit accuracy, i.e., there is no machine number between the computed result and the exact solution. The exact dot product is essential in many algorithms to attain high accuracy.
The main language features and numerical tools of ACRITH-XSC are presented and illustrated by some typical examples. Differences to Fortran 90 are noted where appropriate. A complete sample program for computing continuous bounds on the solution of an initial value problem is given at the end.
Homepage: http://www2.math.uni-wuppertal.de/~xsc/xsc/history.html
Keywords: programming language ACRITH-XSC; numerical algorithms; FORTRAN 77; interval arithmetic; exact dot product
Related Software: C-XSC; C-XSC 2.0; PASCAL-XSC; INTLIB; INTLAB; FORTRAN-SC; INTBIS; ADOL-C; Algorithm 693; VPI; mctoolbox; BLAS; PROFIL/BIAS; FORTRAN-XSC; PCOMP; INTPAK; Maple; LANCELOT; AQUARELS; Algorithm 719
Cited in: 48 Publications

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
ACRITH-XSC. A Fortran-like language for verified scientific computing. Zbl 0801.68019
Walter, Wolfgang V.
1993
all top 5

Cited by 46 Authors

10 Rump, Siegfried Michael
6 Plum, Michael
4 Kulisch, Ulrich W.
4 Schulte, Michael J.
3 Krämer, Walter
2 Corliss, George F.
2 Davidenkoff, Alexander
2 Herzberger, Jürgen P.
2 Jerrell, Max E.
2 Kearfott, Baker
2 Swartzlander, Earl E. jun.
1 Akkas, Ahmet
1 Auzinger, Winfried
1 Bleher, J. Hartmut
1 Burley, James Craig
1 Carstensen, Carsten
1 Christiansen, Søren
1 Črepinšek, Ljubomir
1 Dawande, Milind W.
1 Geörg, Stefan
1 Göhlen, Michael
1 Hammer, Rolf
1 Hocks, Matthias
1 Hofschuster, Werner
1 Hormigo, Javier
1 Hu, Chenyi
1 Jansson, Christian
1 Jaulin, Luc
1 Jüllig, H.-P.
1 Kleinman, Ralph Ellis
1 Krope, Jurij
1 Lipuš, L.
1 Metzger, Michael
1 Nakao, Mitsuhiro T.
1 Nievergelt, Yves
1 Petković, Miodrag S.
1 Ratz, Dietmar
1 Schröder, Johann
1 Stetter, Hans J.
1 Ullrich, Christian P.
1 Villalba, Julio
1 Walster, G. William
1 Walter, Eric
1 Walter, Wolfgang
1 Walter, Wolfgang V.
1 Zelov, Vitaly
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Cited in 16 Serials

11 Computing
4 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)
4 ACM Transactions on Mathematical Software
4 Reliable Computing
2 ZAMP. Zeitschrift für angewandte Mathematik und Physik
2 Linear Algebra and its Applications
2 Computational Economics
1 Mathematics of Computation
1 Automatica
1 Wissenschaftliche Zeitschrift
1 Applied Numerical Mathematics
1 Japan Journal of Applied Mathematics
1 Numerical Algorithms
1 ZOR. Zeitschrift für Operations Research
1 Interval Computations
1 IEEE Transactions on Antennas and Propagation
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Cited in 17 Fields

41 Numerical analysis (65-XX)
13 Computer science (68-XX)
6 Ordinary differential equations (34-XX)
4 Partial differential equations (35-XX)
3 Operations research, mathematical programming (90-XX)
2 Special functions (33-XX)
1 Field theory and polynomials (12-XX)
1 Linear and multilinear algebra; matrix theory (15-XX)
1 Real functions (26-XX)
1 Functions of a complex variable (30-XX)
1 Statistics (62-XX)
1 Mechanics of deformable solids (74-XX)
1 Fluid mechanics (76-XX)
1 Optics, electromagnetic theory (78-XX)
1 Classical thermodynamics, heat transfer (80-XX)
1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
1 Systems theory; control (93-XX)

Citations by Year