Convergence theorems for block splitting iterative methods for linear systems
Journal of Computational and Applied Mathematics
Convergence of General Nonstationary Iterative Methods for Solving Singular Linear Equations
SIAM Journal on Matrix Analysis and Applications
A new splitting and preconditioner for iteratively solving non-Hermitian positive definite systems
Computers & Mathematics with Applications
Modified parallel multisplitting iterative methods for non-Hermitian positive definite systems
Advances in Computational Mathematics
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In the convergence theory of multisplittings for symmetric positive definite (s.p.d.) matrices it is usually assumed that the weighting matrices are scalar matrices, i.e., multiples of the identity. In this paper, this restrictive condition is eliminated. In its place it is assumed that more than one (inner) iteration is performed in each processor (or block). The theory developed here is applied to nonstationary multisplittings for s.p. d. matrices, as well as to two-stage multisplittings for symmetric positive semidefinite matrices.