Formally Verifed Numerical Methods

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• Andrew Appel (Princeton University)
• Wednesday 06 July 2022, 09:30-10:30
• Seminar Room 1, Newton Institute.

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VS2W01 - Vistas in Verified Software

To formally and foundationally verify correctness and accuracy of numerical software, we take a layered, end-to-end approach: prove that the C program correctly implements a floating-point functional model, prove that this float model accurately approximates a real-valued discretized functional model; prove that the real-valued functional model finds sufficiently accurate solutions to the mathematical problem. (Discretized means, e.g., finite time-steps or a finite spatial mesh.) We compose all these proofs into a single main theorem in Coq, stating an overall quantitative accuracy bound for the final result. We demonstrate the method on an ordinary differential equation initial value problem (ODE IVP ).  Co-authors: names and affiliations: Ariel E. Kellison (Cornell)  

This talk is part of the Isaac Newton Institute Seminar Series series.

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