Method
NumCosmoMathSBesselOdeOperatorget_last_deriv_error
Declaration [src]
gdouble
ncm_sbessel_ode_operator_get_last_deriv_error (
NcmSBesselOdeOperator* op,
guint ell_idx
)
Description [src]
Bound on the roundoff left in the endpoint derivatives of the last solve for that
multipole: $\sum_j j^2 |a_j| / h$, which multiplied by the machine epsilon bounds
the absolute error of $u’(x_a)$ and $u’(x_b)$. Those are formed as $u’(\pm 1) =
(1/h)\sum_j (\pm 1)^{j+1} j^2 a_j$, and under NCM_SBESSEL_ODE_CONSTRAINT_TAU any
homogeneous content the truncation admitted cancels in that sum, exactly but not in
floating point —- so this is what survives, and it is what limits the accuracy of a
boundary functional built from the derivatives.
Measured against a reference on panels carrying admitted homogeneous content, the bound is 2 to 27 times above the realized error over 84 orders of magnitude, and never below it. It accounts for that error alone: on a panel where the constraint is valid the error is dominated by the forcing’s own fit instead, and this quantity is far smaller than it.