Comparison theorems for iterative methods based on strong splittings. (English) Zbl 0614.65030

By means of splittings [M]-[N] of an \(n\times n\) interval matrix [A] and by using the interval Gaussian algorithm iterative processes are constructed to enclose the set of solutions of linear systems \(Ax=b\) where A varies in [A] and b varies in a given interval vector [b]. For [A] and [M] being interval M matrices and for [N] containing only nonnegative elements convergence of these methods is proved. The iterative processes associated with two of such splittings are compared with respect to some bounds of their asymptotic convergence factor and with respect to their fixed points.
Reviewer: G.Alefeld


65F10 Iterative numerical methods for linear systems
65G30 Interval and finite arithmetic
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