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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  -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: Institute of Computational Technologies SB RAS
Address: 630090, Russia, Novosibirsk, Ac. Lavrentiev ave, 6
Phone Office: (3832) 30 86 56
E-mail: shary@ict.nsc.ru
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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