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Clarify scope of coefficient positivity in log assessment

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Emily Boudreaux
2026-09-19 10:49:29 -04:00
parent 549b1a761d
commit a34e67bd4b
1 changed files with 2 additions and 2 deletions
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experiments/LOG_DENSITY_ASSESSMENT_2026-09-19.md
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@@ -56,8 +56,8 @@ This retains the original roots whose coefficient vectors are positive. The
Gauss-Legendre nodal basis has sign-changing basis functions, so positive `r_j` Gauss-Legendre nodal basis has sign-changing basis functions, so positive `r_j`
does not imply nonnegative `rho_h`. In particular, taking logarithms of the does not imply nonnegative `rho_h`. In particular, taking logarithms of the
already-positive coefficients at the measured n=1.5 root and applying this already-positive coefficients at the measured n=1.5 root and applying this
coordinate change would reproduce its negative polynomial exactly. No additional coordinate change would reproduce its negative polynomial exactly. Requiring
constraint on positive coefficients removes that root. positive coefficients alone does not remove that root.
### A pointwise exponential of an independent FE field ### A pointwise exponential of an independent FE field