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Convergence for nonnegative double splittings of matrices. (English) Zbl 1232.65056
The authors consider n by n systems of linear equations with regular matrix A and double splittings A=P-R-S leading to 2-step iterations Px i+1 =Rx i +Sx i-1 . They prove convergence theorems like “a nonnegative double splitting is convergent iff the simple splitting (A=P-(R+S)) is” and comparison theorems for different double splittings of the same or of different matrices A. Explicit examples concern 2 by 2 matrices, there is no result on an advantage of double over simple splittings.
65F10Iterative methods for linear systems
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