Ten Digits on a Train: AI-Assisted Verification of Two Eigenvalue Problems
Accurate numerical eigenvalues are often difficult to certify, especially in singular or non-normal settings. This article reports a human--AI collaboration on two such computations. For a singular self-adjoint Schrödinger operator, a verified zero count and Dirichlet--Neumann bracketing certify the complete negative spectrum to ten decimal places. For a delicate non-normal atom--molecule benchmark, a previously unresolved resonance pair is separated, with each member enclosed to ten digits. The second result is achieved not by increasing the precision of one-way shooting, but by reformulating the problem as a global matching system for projective solution lines. The infinite tail is enco...
| Authors | Matthew J. Colbrook |
|---|---|
| Primary category | math.NA |
| Published | 22 June 2026 |
| Last updated at source | 22 June 2026 |
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