= Finite observations do not certify Richardson extrapolation accuracy
<Richardson extrapolation> cancels a specified leading term in an <asymptotic expansion>, but an unquantified remainder does not certify a numerical error at two finite parameter values. For any positive distinct parameters $h_1,h_2$ and prescribed observations $v_1,v_2$, every candidate <limit> $L$ can be made consistent with a model $E(h)=L-ch^2-dh^3$: choose $c,d$ to solve $ch_i^2+dh_i^3=L-v_i$ for $i=1,2$. The coefficient <matrix> has nonzero <determinant> $h_1^2h_2^2(h_2-h_1)$. Thus the observations alone cannot identify $L$, even though every model has exactly the advertised $O(h^3)$ remainder in <Big O notation>. Quantitative remainder bounds or additional information are needed for an error certificate.
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