Convergence Properties of the Successive Extrapolated Relaxation (S.E.R.) Method

Extrapolation methods to accelerate convergence of a sequenceof iterates are investigated. A transformation formula derivedfrom the related deterministic sequence is modified so thatit may be used for the stochastic sequences. The S.E.R. method,which is related to Aitken's ² process, is discussed. For linearlyconvergent sequences it is shown that S.E.R. not only will convergeif the original sequence converges, but will converge to thesame limit. An analysis of the bounds for the convergence andthe perturbations is made for Aitken's ² process, S.E.R. andS.E.O.R. The method is applicable to convergent and locallyconvergent vector sequences.     

Demagnetization Matrices for Cylindrical Bodies

Demagnetization matrices are defined for cylindrical rings.It is assumed that the magnetization pattern has cylindricalsymmetry. An examination of the symmetry properties of thesematrices shows that certain components are zero. The componentsof the demagnetization matrices can be expressed as ellipticintegrals. For rings of rectangular cross section then the resultsare expressed in terms of the parameters which describe thering. Computational algorithms are discussed.