Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
A Generic Library for Floating-Point Numbers and Its Application to Exact Computing
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
A Parametric Error Analysis of Goldschmidt's Division Algorithm
ARITH '03 Proceedings of the 16th IEEE Symposium on Computer Arithmetic (ARITH-16'03)
Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
Formal Verification of Floating-Point Programs
ARITH '07 Proceedings of the 18th IEEE Symposium on Computer Arithmetic
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Combining Coq and Gappa for Certifying Floating-Point Programs
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
The Why/Krakatoa/Caduceus platform for deductive program verification
CAV'07 Proceedings of the 19th international conference on Computer aided verification
Static analysis of numerical algorithms
SAS'06 Proceedings of the 13th international conference on Static Analysis
Combining Coq and Gappa for Certifying Floating-Point Programs
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
Formal proof of a wave equation resolution scheme: the method error
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Verification of a heat diffusion simulation written with orléans skeleton library
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part II
Improving real analysis in coq: a user-friendly approach to integrals and derivatives
CPP'12 Proceedings of the Second international conference on Certified Programs and Proofs
Wave Equation Numerical Resolution: A Comprehensive Mechanized Proof of a C Program
Journal of Automated Reasoning
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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.