Modified successive overrelaxation (MSOR) and equivalent 2-step iterative methods for collocation matrices

Modified Successive Overrelaxation (MSOR) and Equivalent 2-Step Iterative Methods for Collocation Matrices

We consider a class of consistently ordered matrices which arise from the discretization of Boundary Value Problems (BVPs) when the finite element collocation method, with Hermite elements, is used. Through a recently derived equivalence relationship for the asymptotic rates of convergence of the Modified Successive Overrelaxation (MSOR) and a certain 2-step iterative method, we determine the o...

On the modified successive overrelaxation method

Keywords: SOR KSOR MSOR MKSOR and iterative methods a b s t r a c t New forms of the modified successive overrelaxation (MSOR); MKSOR, MKSOR1 and MKSOR2 are introduced. These forms depend on the updated successive overrelaxation method (KSOR) and the combination of the SOR and the KSOR methods. We present analysis of the convergence of the MKSOR methods with fixed parameters for solving linear ...

Supremum-Norm Convergence for Step-Asynchronous Successive Overrelaxation on M-matrices

Step-asynchronous successive overrelaxation updates the values contained in a single vector using the usual Gauß–Seidel-like weighted rule, but arbitrarily mixing old and new values, the only constraint being temporal coherence— you cannot use a value before it has been computed. We show that given a nonnegative real matrix A, a σ ≥ ρ(A) and a vector w > 0 such that Aw ≤ σw, every iteration of ...

A!successive Overrelaxation Iterative Technique for an Adaptive Equalizer

i

Two modified Jacobi methods for M-matrices