Abstract
The Baur-Strassen method implies L(∇f) ⩽ 4L(f), where L(f) is the complexity of computing a rational function f by arithmetic circuits, and ∇f is the gradient of f. We show that L(∇ f) ⩽ 3L(f) + n, where n is the number of variables in f. In addition, the depth of a circuit for the gradient is estimated.
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Original Russian Text © I.S. Sergeev, 2007, published in Diskretnyi Analiz i Issledovanie Operatsii, Ser. 1, 2007, Vol. 14, No. 4, pp. 57–75.
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Sergeev, I.S. On the complexity of the gradient of a rational function. J. Appl. Ind. Math. 2, 385–396 (2008). https://doi.org/10.1134/S1990478908030095
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DOI: https://doi.org/10.1134/S1990478908030095