Geodesic
The arithmetic computational complexity of linear transforms
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2014), pp. 24-31

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Quadratic and superquadratic estimates are obtained for the complexity of computations of some linear transforms by circuits over the base $\{x+y \}\cup \{ax: \vert a \vert \leq C \}$ consisting of addition and scalar multiplications on bounded constants. Upper bounds $O(n\log n)$ of computation complexity are obtained for the linear base $\{ax+by: a,b \in {\mathbb R}\}$. Lower bounds $\Theta(n\log n)$ are obtained for the monotone linear base $\{ax+by: a, b > 0\}$. 
@article{VMUMM_2014_6_a3,
     author = {S. B. Gashkov},
     title = {The arithmetic computational complexity of linear transforms},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {24--31},
     publisher = {mathdoc},
     number = {6},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2014_6_a3/}
}
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S. B. Gashkov. The arithmetic computational complexity of linear transforms. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2014), pp. 24-31. http://geodesic.mathdoc.fr/item/VMUMM_2014_6_a3/