The Young–Eidson Algorithm: Applications and Extensions
APOSTOLOS HADJIDIMOS, Dimitrios Noutsos · SIAM Journal on Matrix Analysis and Applications · 1990
In this paper it is assumed that the point (or block) Jacobi matrix B associated with the matrix A is weakly 2-cyclic consistently ordered with complex, in general, eigenvalue spectrum $\sigma (B)$ lying in the interior of the infinite unit strip. It is then our objective to apply and extend the Young–Eidson algorithm in order to determine the real optimum relaxation factor in the following two cases: (i) In the case of the successive overrelaxation (SOR) matrix associated with A when $\sigma (B)$ lies in a “bow-tie” region, and (ii) in the case of the symmetric SOR (SSOR) matrix associated with A. In the latter case a number of numerical examples are given. It is noted that as a by-product of (ii) both the relaxation factor for the SSOR matrix corresponding to a “bow-tie” spectrum $\sigma (B)$ and the optimum pairs of the relaxation factors for the unsymmetric SOR (USSOR) matrix associated with A are also obtained.