Research project
Bounds for the Trefethen Constant
Compute rigorous upper and lower bounds for the operator norm in Trefethen’s third hundred-digit challenge problem: the norm of the infinite matrix formed by arranging along successive antidiagonals.
Current state
The manuscript encloses the constant in an interval of width , certifying 870 decimal places. The argument combines Gaussian quadrature, residual and resolvent estimates, and an explicit correction for the infinite tail. The repository includes the proof, exact certificate data, and verification programs.
The norm is approximately . Certifying further digits requires controlling quadrature and rounding errors as well as the contribution of the infinite tail.
Future plans
The numerical bottleneck is the sampled norm estimate. Reaching 10,000 certified decimal places and completing a full-size rerun of the public verifier remain open tasks.
Details
- Phase
- Public manuscript · 870 certified decimal places
- Domain
- Numerical analysis · operator theory · rigorous computation
- My role
- Research direction
Artifacts
- Paper (PDF) manuscript
- Repository and verification instructions repository
- Exact interval certificate