Article information

1999 , Volume 4, ¹ 4, p.82-110

Shary S.P.

Outer estimation of generalized solution sets to interval linear systems

The paper advances various techniques for outer interval estimation of the generalized ÀÅ-solution sets to interval linear systems. We propose ``algebraic approach" in which the outer estimation problem is reduced to the problem of computing algebraic solutions of an auxiliary equation in Kaucher complete interval arithmetic. The second main result of the paper is generalized interval Gauss-Seidel iteration. We examine the applicability of the techniques proposed, present the convergence analysis for Gauss-Seidel iteration, and prove the optimality of its results for interval linear systems with M-matrices.

[full text] Classificator Msc2000:
*65F10 Iterative methods for linear systems
65G30 Interval and finite arithmetic
Classificator Computer Science:
*G.1.0 General (Numerical Analysis)
G.1.3 Numerical Linear Algebra

Keywords: interval linear system, generalized solution set, outer estimation, interval arithmetic, complete interval arithmetic

Author(s):
Shary Sergey Petrovich
Dr. , Senior Scientist
Position: Leading research officer
Office: Federal Research Center for Information and Computational Technologies
Address: 630090, Russia, Novosibirsk, Ac. Lavrentiev ave, 6
Phone Office: (3832) 30 86 56
E-mail: shary@ict.nsc.ru
SPIN-code: 9938-9344


Bibliography link:
Shary S.P. Outer estimation of generalized solution sets to interval linear systems // Computational technologies. 1999. V. 4. ¹ 4. P. 82-110
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