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.\parWith 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.\parThe 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.

References in zbMATH (referenced in 40 articles , 1 standard article )

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  1. Krämer, Walter: Multiple/arbitrary precision interval computations in C-XSC (2012)
  2. Rump, Siegfried M.: Fast interval matrix multiplication (2012)
  3. Nievergelt, Yves: Scalar fused multiply-add instructions produce floating-point matrix arithmetic provably accurate to the penultimate digit (2003)
  4. Kulisch, Ulrich W.: Advanced artihmetic for the digital computer. Design of arithmetic units (2002)
  5. Rump, Siegfried M.: Computational error bounds for multiple or nearly multiple eigenvalues (2001)
  6. Hofschuster, Werner; Krämer, Walter: Mathematical function software on the web -- are such codes useful for verification algorithms? (2000)
  7. Corliss, George F.: SCAN-98 collected bibliography (1999)
  8. Schulte, Michael J.; Zelov, Vitaly; Akkas, Ahmet; Burley, James Craig: The interval-enhanced GNU Fortran compiler (1999)
  9. Rump, Siegfried M.: A note on epsilon-inflation (1998)
  10. Jerrell, Max E.: Automatic differentiation and interval arithmetic for estimation of disequilibrium models (1997)
  11. Christiansen, Søren; Kleinman, Ralph E.: On a misconception involving point collocation and the Rayleigh hypothesis (1996)
  12. Schulte, Michael J.; Swartzlander, Earl E.jun.: Software and hardware techniques for accurate, self-validating arithmetic (1996)
  13. Walster, G.William: Stimulating hardware and software support for interval arithmetic (1996)
  14. Corliss, George F.: Guaranteed error bounds for ordinary differential equations (1995)
  15. Kearfott, R.B.: A Fortran 90 environment for research and prototyping of enclosure algorithms for nonlinear equations and global optimization (1995)
  16. Schulte, Michael J.; Swartzlander, Earl E.jun.: A software interface and hardware design for variable-precision interval arithmetic (1995)
  17. Jerrell, Max E.: Global optimization using interval arithmetic (1994)
  18. Kearfott, R.B.; Dawande, M.; Hu, C.: Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library (1994)
  19. Carstensen, C.; Petković, M.S.: On some interval methods for algebraic, exponential and trigonometric polynomials (1993)
  20. Jaulin, Luc; Walter, Eric: Set inversion via interval analysis for nonlinear bounded-error estimation (1993)

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