ACRITHXSC
swMATH ID:  15 
Software Authors:  Walter, Wolfgang V. 
Description:  ACRITHXSC is a Fortranlike programming language designed for the development of selfvalidating 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, selfvalidating numerical techniques have been successfully applied to a variety of engineering problems in soil mechanics, optics of liquid crystals, groundwater modelling and vibrational mechanics where conventional floatingpoint methods have failed. With few exceptions, ACRITHXSC is an extension of FORTRAN 77. Various language concepts which are available in a ACRITHXSC can also be found in a more or less similar form in Fortran 90. Other ACRITHXSC 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”, ACRITHXSC provides a special notation which guarantees that expressions of this type are evaluated with leastbit 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 ACRITHXSC 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.uniwuppertal.de/~xsc/xsc/history.html 
Keywords:  programming language ACRITHXSC; numerical algorithms; FORTRAN 77; interval arithmetic; exact dot product 
Related Software:  CXSC; CXSC 2.0; PASCALXSC; INTLIB; INTLAB; FORTRANSC; INTBIS; ADOLC; Algorithm 693; VPI; mctoolbox; BLAS; PROFIL/BIAS; FORTRANXSC; PCOMP; INTPAK; Maple; LANCELOT; AQUARELS; Algorithm 719 
Cited in:  48 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

ACRITHXSC. A Fortranlike language for verified scientific computing. Zbl 0801.68019 Walter, Wolfgang V. 
1993

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Cited by 46 Authors
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Cited in 16 Serials
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