Abstract
We present a case study of a formal verification of a numerical program that computes the discretization of a simple partial differential equation. Bounding the rounding error was tricky as the usual idea, that is to bound the absolute value of the error at each step, fails. Our idea is to find out a precise analytical expression that cancels with itself at the next step, and to formally prove the correctness of this approach.
This work was funded by the French national research organization (ANR), by the CerPAN (ANR-05-BLAN-0281-04) and F\(\oint\)st (ANR-08-BLAN-0246-01) projects.
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Boldo, S. (2009). Floats and Ropes: A Case Study for Formal Numerical Program Verification. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds) Automata, Languages and Programming. ICALP 2009. Lecture Notes in Computer Science, vol 5556. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02930-1_8
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DOI: https://doi.org/10.1007/978-3-642-02930-1_8
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