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On the solution of interval linear systems. (English) Zbl 0753.65030
This paper is concerned with one of the standard problems in numerical linear algebra: to compute lower and upper bounds for the solution of a system of linear equations in the presence of rounding errors and/or tolerances in the input data. Here iterative methods are considered. The author presents an algorithm for solving the stated problem with interval input data and interval operations. In particular practicable stopping criteria are discussed.
This algorithm is compared with an algorithm of A. Neumaier [Interval methods for systems of equations (1990; Zbl 0715.65030)]. A suitable combination of both yields tight bounds for input intervals of small and large diameter. In addition, tolerance regions different from intervals are considered, namely simplices. Some interesting examples show the difference between using intervals and using simplices.

MSC:
65F10 Iterative numerical methods for linear systems
65G30 Interval and finite arithmetic
Software:
ACRITH-XSC
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References:
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