We present a Céa type inequality which is the starting point for error estimation.
The favorable properties of the spatial discretization technique suggest that this may be the starting point for an error-controlled sensitivity analysis in higher dimensions.
The new optimization methods benefit from the soft computing capabilities of global optimization and multi-objective optimization rather than choosing a starting point by trial and error and combining multiple criteria into a single criterion in conventional lens design techniques.
We take advantage of GA's capability of global optimization and multi-objective optimization against two serious problems in conventional lens optimization techniques: (1) choosing a starting point by trial and error, and (2) combining multiple criteria to a single criterion.
Traditional inquiries tend to stop once human error has been found, whereas a systems approach treats human error as the starting point and examines the whole context in which the operator was working to see how this impacted on their ability to perform well.
A major result of this paper is a categorization of the sources of faults into a formal taxonomy that provides a starting point for future research into error-based approaches to improving software quality.
In Fig. 7, we examine the numerical periodicity with several methods and calculate the error between the starting point ((q_{1}(0),q_{2}(0))=(0.4,0)) and the numerical solution at time (2kpi) ((k=1, ldots,500)) by using the Matlab built-in function for the cubic spline interpolation.
As a starting point, the elements of the measurement error vector (ε i ) are assumed independent.
The solutions found by GD are only marginally closer to the known solution than the 1% starting point, but have dramatically lower RMS error.
The BP neural network training begins with a starting point for the tangent gradually reaching the minimum error.
