codecov[bot]
commented
1 month ago Codecov Report
All modified and coverable lines are covered by tests :white_check_mark:
Project coverage is 98.54%. Comparing base (
d5bbb69) to head (a529373).
Additional details and impacted files
```diff @@ Coverage Diff @@ ## master #111 +/- ## ======================================= Coverage 98.53% 98.54% ======================================= Files 7 7 Lines 682 686 +4 ======================================= + Hits 672 676 +4 Misses 10 10 ```:umbrella: View full report in Codecov by Sentry.
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Should fix #109.
Our arbitrary-precision eigensolver works by Newton's method on $\det(J - \lambda I)$ where $J$ is the Jacobi matrix, but the problem is that the determinant calculation easily underflows. However, since what we actually want is only the ratio $\det(J - \lambda I) / \det'(J - \lambda I)$ (the Newton step), we can rescale to this ratio at each step of the tridiagonal-determinant iteration to suppress under/ovrerflow.
On a separate note, the Newton iteration was missing the
breakstatement on the convergence check, so it was taking 1000x longer than necessary!