Error Analysis in Numerical Modeling
In numerical simulation or modeling of real systems, error analysis is concerned with the changes in the output of the model as the parameters to the model vary about a mean.
For instance, in a system modeled as a function of two variables . Error analysis deals with the propagation of the numerical errors in and (around mean values and ) to error in (around a mean ).
In numerical analysis, error analysis comprises both forward error analysis and backward error analysis. Forward error analysis involves the analysis of a function which is an approximation (usually a finite polynomial) to a function to determine the bounds on the error in the approximation; i.e., to find such that . Backward error analysis involves the analysis of the approximation function, to determine the bounds on the parameters such that the result .
Error analysis in SLA was established in the 1960s by Stephen Pit Corder and colleagues. Error analysis was an alternative to contrastive analysis, an approach influenced by behaviorism through which applied linguists sought to use the formal distinctions between the learners' first and second languages to predict errors. Error analysis showed that contrastive analysis was unable to predict a great majority of errors, although its more valuable aspects have been incorporated into the study of language transfer. A key finding of error analysis has been that many learner errors are produced by learners making faulty inferences about the rules of the new language.
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