Sentence examples for bounds for the errors from inspiring English sources
Our approach can compute bounds for the errors induced by dimension reduction, defeaturing or both in combination.
One seeks to minimize bounds for the errors in the calculated results obtained from a given set of input data, exploiting analytical relations.
Sadabadi et al. [24] estimated the upper bounds for the errors by using the relationship among the segment length, average speed, and travel time and showed that the travel time measurement error is negligible when the average speed is around 45 kmph and the distance between two detectors is 2 3 miles.
In order to reduce the computational complexity, we present a combination of domain decomposition and balanced truncation model reduction which allows explicit error bounds for the error between the reduced order and the fine-scale optimization problem.
The work contains: details of the discretisation using non-uniform order mixed finite elements of arbitrarily high order; a new local post-processing scheme for the primary variable; the use of the post-processing scheme in the derivation of new, fully computable bounds for the error in the flux variable; and, an hp-adaptive refinement strategy based on the a posteriori error estimator.
We present an a posteriori finite element procedure that provides inexpensive, rigorous, accurate, and constant-free lower and upper bounds for the error in the outputs – engineering quantities of interest – predicted by (Lagrangian) reduced-order approximations to coercive elliptic partial differential equations.
In Section 3, we derive both (L^{2} -(H^{1}) a posteriori upper error bounds for the error estimates of the control, the state, and the co-state.
As applications, we find several complete monotonicity properties for the functions involving the gamma function and provide the bounds for the error function.
