Geodesic
Error estimation of computing a~multivariable function and its gradient
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 1, pp. 77-88.

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Graphs for the calculation of composite functions of multiple variables, the duality principle for obtaining the composite function gradient are described. Algorithms for the estimation of the computation error of the composite function and its gradient are presented. 
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M. Yu. Senashova. Error estimation of computing a~multivariable function and its gradient. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 1, pp. 77-88. http://geodesic.mathdoc.fr/item/SJVM_2007_10_1_a4/

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