DefinitionError analysis refers to the study of uncertainties, inaccuracies or deviations in mathematical computations, measurements or numerical simulations, and is key to the success of scientific investigations. Error analysis is about the identification of errors and their sources, the estimation of error bounds attributed to the errors, and an appraisal of the effects of errors on the validity and reliability of results. Error analysis methods may use error propagation, Taylor series approximation, numerical differentiation/integration, and statistical methods (e.g., such as confidence intervals and hypothesis testing). In many fields of science and engineering, experimental sciences, and finance, error analysis is used to evaluate the reliability and accuracy of calculations and predictions. For Example: In numerical integration, the error analysis constitutes the comparison of the approximate integral obtained with the help of numerical methods to the exact integral (or anti-derivative) for the purpose of assessing the accuracy or the rate of convergence of the numerical solution.
