# residual error

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Related to residual error: Residuals

## re·sid·u·al er·ror

the estimated discrepancy between the actual measured datum and the value for that value computed after a model has been fitted to the set of the data by an estimator.
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The optimal values for the convergence-control parameters can be obtained by the minimum of total average squared residual error. The total average squared residual error [E.sup.t.sub.k]([c.sup.f.sub.0], [c.sup.s.sub.0], [c.sup.[theta].sub.0], [c.sup.[theta].sub.0]) is minimized by using symbolic computation software MaThemafica.
The residual error is used in establishing the suitable convergence controlling parameter [??].
Experiments are performed by the DDM-FE-BI-MLFMA without and with ABC-SSOR preconditioner, respectively and the residual error is set to 0.005.
The sub-matrix Equations (6) and (12) can be solved one by one until the relative residual error is less than a given value.
Case 2 assessed the effect of the SLOPE parameter when residual error was set to a value typical of qHTS data [[sigma] = 25%; see Supplemental Material, Table S1 (http://dx.doi.org/10.1289/ehp.1104688)].
Let the residual error series be [[epsilon].sup.(0)] = ([[epsilon].sup.(0)](1), [[epsilon].sup.(0)](2), ..., [[epsilon].sup.(0)](n)), where [[epsilon].sup.(0)](k) means the residual error at k-th time and [[epsilon].sup.(0)](k) = [x.sup.(0)](k) - [[??].sup.(0)](k) for k = 1,2, ..., n.
The variance of the pupil level residual errors ([[delta].sup.2.sub.e]) is estimated as 516.35 and the variance of the class level residual error ([[delta].sup.2.sub.u]0) is estimated as 346.67, which means that 40.17% of the variance in arithmetic achievement is explained by differences between classes (intra-class correlation coefficient of .40) indicating that differences between classes might be substantial.
First, we need to estimate the residual error correction terms [[??].sub.ip] (ECT) of equation (4), (5) and (6), then respectively estimate panel dynamic error correction model (7), (8), (9).
After minimizing the residual error, the optimal SCF was equal to 0.7%, providing low standard deviations and residual error.
However, if the problem or application under consideration requires zeroing vector element one by one(sample by sample) Givens rotation is suitable for this job but when multiple vector elements are annihilated(block by block) the Householder transformation is considered best .In this note we apply transpose update method (TUM) and Modified Gram Schmidt approach to compute the weight vector and least squares residual error [e.sup.q.sub.LSREp](n).

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