From Rounding Error Estimation to Automatic Correction with Automatic Differentiation
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Using automatic differentiation (AD) to estimate the propagation of rounding errors in numerical algorithms is classic. We propose a new application of AD to roundoff analysis providing an automatic correction of the first order effect of the elementary rounding errors. We present the main characteristics of this method and significant examples of its application to improve the accuracy of computed results and/or the stability of the algorithm.
KeywordsReverse Mode Floating Point Automatic Differentiation Single Precision Linear Algorithm
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