Parallel iterative methods are studied, and the focus is on linear algebraic systems whose matrix is symmetric and positive definite. The set of unknowns may be viewed as a union of subsets of unknowns (possibly with overlap). The parallel iteration matrix is then formed by a weighted sum of iteration matrices that are associated with splittings of the matrix corresponding to the blocks. When the blocks are from a matrix in dissection form, it can be shown under suitable conditions that the parallel algorithm is convergent. When the multisplitting version of successive over-relaxation (SOR) is used, the SOR parameter is required to be less than $\omega _0 < 2.0$. Calculations done on the Alliant FX/8 multiprocessing/vector computer indicate speedups of nine to ten.