Abstract
Grama–Schmidt's modified algorithm of orthonormalization of the finite-dimensional vectors, intended for creation of mathematical models of linear static objects on the basis of the measured values of their entrance and output variables arriving in system is offered. In the synthesized algorithm instability of the decision in relation to errors of a task of ortonormiruyemy vectors and errors of calculations significantly is reduced. The algorithm of similar appointment was offered in due time to J. Wilkinson, he is well-known and bears his name. Essential advantage of the offered algorithm before Gram's generalized algorithm – Schmidt and Wilkinson is that its application allows to processing measured values of entrance variables arriving in system in real time. Adequacy of models received thus is coordinated with an accuracy of a task of values of variables of modelled object.
Keywords: Grama-Schmidt's algorithm, Wilkinson's algorithm, linear dependence and orthogonalization of vectors, instability of the decision
References
[1] Воеводин В.В. Вычислительные основы линейной алгебры / В.В. Воеводин. – М.: Наука, 1977. – 304 с. [2] Уилкинсон Дж. Справочник алгоритмов на языке АЛГОЛ. Линейная алгебра / Дж. Уилкинсон, К. Райнш; пер. с англ. под ред. д-ра техн. наук проф. Ю.И. Топчеева. – М.: Машиностроение, 1976. – 389 с. [3] Ильин В.А. Линейная алгебра / В.А. Ильин, Э.Г. Поздняк. – М.: Наука, 1974. – 296 с. [4] Светлаков А.А. Обобщенные обратные матрицы: некоторые вопросы теории и применения в задачах автоматизации управления процессами / А.А. Светлаков. – Томск: Изд-во НТЛ, 2003. – 388 с.
