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Understanding the exact errors can help tailor treatments to the individual, or small groups picking the drugs mostly likely to be effective.
Since the exact errors are not known and only the covariance matrices of these errors are known, we need to derive the average MSE matrix.
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In this paper, we present an exact error analysis for circle approximation by Bézier curve.
The analytical finite-element solutions, the exact error expressions and convergence rates are derived.
Then the exact analytical finite difference solutions, the exact error expressions and the exact convergence rates are derived.
This technique produces accurate estimations of the exact error but is not designed to naturally produce upper bounds of the error in energy norm.
While the extended Luenberger observer results from a first order approximation of exact error dynamics, this paper provides an explicit formula for a second order approximation.
For smooth boundary-value problems containing first and second derivatives the error estimates converge to the exact error as the mesh is refined.
To ensure accuracy, grid convergence and to reduce computational time, an adaptive finite-element method driven by asymptotically exact error estimations is used.
Exact error propagation is used to compute the uncertainty in the fitted response function and to treat common data transformations designed to reduce or eliminate the effects of data heteroscedasticity.
The new method is used to obtain exact error estimators to evaluate the effects of various TBCs on the dam reservoir first resonant frequency and hydrodynamic forces acting on the dam upstream face.
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