Interval arithmetic for certified computations
Build a small interval-arithmetic library and use it to certify roots found by numerical solvers.
- Suitable for
- Undergraduate thesis
- Supervision
- Tülay Ayyıldız
- Prerequisites
- Basic numerical analysis; programming
Numerical solvers return approximate roots without guarantees. Interval arithmetic computes with enclosures instead of numbers, and tests such as the interval Newton and Krawczyk operators can prove that a box contains exactly one root.
Goal
Implement interval arithmetic with correct rounding, implement the interval Newton or Krawczyk test, and use them to certify the roots returned by a standard numerical solver.