On the consistency of linear and quadratic systems

A. V. Arutyunov^a, E. V. Kruglova<sup>b

a</sup> Department of Differential Equations, Russian University of Peoples' Friendship, ul. Ordzhonikidze, Moscow, 117923, Russia
^b Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

Abstract: A system of linear inhomogeneous inequalities is examined. An algorithm is presented for isolating all the consistent subsystems in this system that are maximal with respect to inclusion, and justification of this algorithm is given. A criterion for the consistency of a system of quadratic inhomogeneous equations and inequalities is proposed.

Key words: linear inequalities, quadratic inequalities, criterion for consistency,optimal algorithm.

UDC: 519.612

Received: 31.03.2005
Revised: 03.11.2005

 English version: Computational Mathematics and Mathematical Physics, 2006, 46:4, 537–540

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