id: 04078628
dt: j
an: 04078628
au: Galanis, S.; Hadjidimos, A.; Noustos, D.
ti: On the equivalence of the k-step iterative Euler methods and successive
    overrelaxation (SOR) methods for k-cyclic matrices.
so: Math. Comput. Simul. 30, No.3, 213-230 (1988).
py: 1988
pu: Elsevier Science B.V. (North-Holland), Amsterdam
la: EN
cc: 
ut: consistently ordered k-cyclic matrices; successive overrelaxation; Jacobi
    matrix; k-cyclic SOR method; stationary k-step iterative method;
    optimal relaxation factor; region of convergence
ci: Zbl 0487.65018
li: doi:10.1016/0378-4754(88)90001-8
ab: The authors establish the relationship $ω\sp kT\sp k{\cal
    L}\sbω\sp{k-1}=[{\cal L}\sbω+(ω+1)I]\sp k$ connecting the successive
    overrelaxation (SOR) matrix ${\cal L}\sbω$ and the Jacobi matrix T
    associated with a linear system $x=Tx+c$, where T is weakly cyclic of
    index k. Based on this result, they derive an equivalence between the
    k-cyclic SOR method and a certain stationary k- step iterative method
    [cf. {\it W. Niethammer} and {\it R. S. Varga}, Numer. Math. 41,
    177-206 (1983; Zbl 0487.65018)]. By applying the theory of these
    stationary k-step methods, old and new results on the k-cyclic SOR
    method are shown, e.g., the optimal relaxation factor and the region of
    convergence are determined.
rv: M.Eiermann