The Young-Eidson Algorithm: Applications and Extensions
نویسندگان
چکیده
Ahstract In this paper it is assumed that the point (or block) Jacobi manix. B associated with the matrix A is weakly 2-cyclic consistently ordered with complex, in general, eigen-value spectrum, a(B), lying in the interior of the infinite unit strip. It is then our objec~ live to apply and ex.tend 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 a(B) lies in a "bow-tie" region and ti) In the case of the Symmetric SOR (SSOR) matrix associated with A. It is noted that as a by-product of (ti) above both the relaxation factor for the SSOR matrix corresponding to a "bow-tie" spectrum a(8) and the optimum pairs of the relaxation factors for the Unsymmetric SOR (USSOR) matrix associated with A are also obtained.
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