Abstract
We consider linear systems of algebraic equationsSu=f with tridiagonal interval matrixS and interval vector f An interval version of the sweep method allows us to find an interval vector u=(u1, u2,..., u n )T that contains the united set of solutions of the system. In the paper we present estimates of the absolute value and the width of the intervals u i ,i=1, 2,...,n under certain assumptions on the elements of the matrixS that do not include the traditional condition of diagonal dominance. The width estimates are three orders of magnitude narrower, and the assumptions on the system’s coefficients are weaker than those in works published so far.
Abstract
Рассматривается система линейных алгебраических уравненийSu=f с трехдиагональной интервальной матрицейS и интервальным вектором f. Интервальная версия метода прогонки позволяет отыскать интервальный вектор u=(u1, u2,... u n )T, содержащий объединенное множество решений зтой системы. В работе при некоторых ограничениях на злементы матрицыS, не предполагающих традиционного условия диагональног о преобладания, даются оценки абсолютного значения и ширины интервалов u i ,i=1,2,...,n. Оценки ширины на три порядка меньше, а ограничения на козффициенты системы слабее, чем в ранее известных публикациях.
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Ostylovsky, A.N. An estimate of the absolute value and width of the solution of a linear system of equations with tridiagonal interval matrix by the interval sweep method. Reliable Comput 1, 393–401 (1995). https://doi.org/10.1007/BF02391684
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DOI: https://doi.org/10.1007/BF02391684