Convergence for nonnegative double splittings of matrices
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.
scientific article; zbMATH DE number 5988489