Abstract
The additive computation of a system of linear forms can be represented by a sequence of square matrices Q1,...,QT (Qi equals the identity matrix increased or decreased by 1 in one entry). The complexity of the additive computation is the minimal number of matrices in such a representation. A connection between the additive complexity of a system with coefficient matrix A and of a system with coefficient matrix AT is proved.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
J. E. Savage, “An algorithm for the computation of linear forms,” SIAM J. Comp.,3, No. 2, 150–158 (1974).
J. Morgenstern, “On linear algorithms,” in: Theory of Machines and Computations, New York (1971), pp. 59–66.
D. Yu. Grigor'ev, “Application of separability and independence notions for proving lower bounds of circuit complexity,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,60, 38–48 (1976).
R. É. Val'skii, “On the minimal number of multiplications required to compute a given power,” Probl. Kibern.,2, 73–74 (1959).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 105, pp. 53–61, 1981.
Rights and permissions
About this article
Cite this article
Sidorenko, A.F. Complexity of additive computations of systems of linear forms. J Math Sci 22, 1310–1315 (1983). https://doi.org/10.1007/BF01084394
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01084394