Error-reduction algorithm

Subsequently, other workers developed numerous variations and generalizations of the basic method. Most methods can be summarized by the accompanying generalized error-reduction algorithm. 

This algorithm has been called an error-reduction algorithm because it has been shown for a particular case (and it may be generally true) that the error can only decrease with succeeding iterations (Liu and Gallagher, 1974). Note, however, that the error does not necessarily decrease to zero or even to the desired minimum residual value that is based on noise. 

Singh DK, Panigrahi PK (2010) Improved digital holographic reconstmction algorithm for depth error reduction and elimination of out-of-focus particles. Opt Express 18(3) 2426... 

The use of complex models is hindered by two obstacles. First, the models contain large numbers of unknown kinetic parameters regression to determine the parameters of complex nonlinear models is both difficult and unreliable. Secondly, because of their sheer size and the presence of multiple time-scales, these models are difficult to solve. For these reasons, model simplification and order reduction are central problems for complex reaction systems. Ideally, a model order reduction algorithm would have broad applicability, permit analysis at several levels of detail, and provide an assessment of the modeling error. 

Condition 2 either requires a large number of extra experiments or a reduction to 25 wavelengths. There have been a number of algorithms that have been developed to reduce the wavelengths to the most significant ones, so enabling inverse models to be used, but there is no real advantage over classical models unless very specific information is available about error distributions. 

The design of optimal second-order and higher order FDTD algorithms with dispersion-relation-preserving (DRP) properties constitutes a promising tool for the drastic reduction of dispersion errors, as firstly presented and extensively investigated in [55, 56]. Actually, the key... 

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