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New methods for evaluating the validity of the results of mathematical computations

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  • Vignes, J.

Abstract

From a mathematical standpoint, numerical methods can be divided in two classes: (i) Direct methods, which give an exact result after some finite number of computations, and (ii) approximate methods, which only give an approximate result after any finite number of computations.

Suggested Citation

  • Vignes, J., 1978. "New methods for evaluating the validity of the results of mathematical computations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 20(4), pages 227-249.
    • Handle: RePEc:eee:matcom:v:20:y:1978:i:4:p:227-249
    DOI: 10.1016/0378-4754(78)90016-2
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    References listed on IDEAS

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    1. Alt, René, 1978. "Error propagation in fourier transforms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 20(1), pages 37-43.
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    Cited by:

    1. Abadie, J. & Dekhli, F., 1988. "A variant of the CESTAC method and its application to constrained optimization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 519-529.
    2. Albertsen, Niels Christian & Chesneaux, Jean-Marie & Christiansen, Søren & Wirgin, Armand, 1999. "Comparison of four software packages applied to a scattering problem1Professor Ralph E. Kleinman, University of Delaware, USA, in memoriam.1," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 48(3), pages 307-317.
    3. Alt, René, 1988. "Floating-point error propagation in iterative methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 505-517.
    4. Ton-That, Long, 1988. "Numerical accuracy control in fixed-point arithmetic," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 553-561.
    5. Bois, P. & Vignes, J., 1980. "A software for evaluating local accuracy in the fourier transform," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 22(2), pages 141-150.
    6. Alt, R. & Lamotte, J.-L., 2001. "Experiments on the evaluation of functional ranges using a random interval arithmetic," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 56(1), pages 17-34.
    7. Vergnes, J. & Dumontet, J., 1979. "Finding an optimal partition for a numerical integration using the trapezoidal rule," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 21(2), pages 231-241.
    8. Vergnes, J., 1980. "Determination d'un pas optimum d'integration pour la methode de Simpson," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 22(3), pages 177-188.
    9. Vignes, Jean, 1984. "An efficient implementation of optimization algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 26(3), pages 243-256.
    10. Toutounian, Faezeh, 1988. "Practical methods for evaluating the accuracy of the eigenelements of a symmetric matrix," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 493-504.
    11. Alliot, Nicole, 1988. "Data error analysis in unconstrained optimization problems with the CESTAC method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 531-539.
    12. Vignes, J., 1993. "A stochastic arithmetic for reliable scientific computation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(3), pages 233-261.
    13. Pichat, M., 1988. "All possible computed results in correct floating-point summation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 541-552.
    14. Salkuyeh, Davod Khojasteh & Toutounian, Faezeh & Yazdi, Hamed Shariat, 2008. "A procedure with stepsize control for solving n one-dimensional IVPs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(2), pages 167-176.

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    1. Alt, René, 1988. "Floating-point error propagation in iterative methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 505-517.

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