On the exact \(p\)-cyclic SSOR convergence domains (Q1906797)

This paper considers convergence domains for symmetric successive overrelaxation (SSOR) applied to a block \(p\)-cyclic, consistently ordered matrix \(A \in \mathbb{C}^{n,n}\). If \(B\) is the block Jacobi matrix and \(S_\omega\) the block SSOR matrix associated with \(A\), \textit{A. Hadjidimos} and \textit{M. Neumann} [J. Comput. Appl. Math. 33, No. 1, 35-52 (1990; Zbl 0716.65027)] derived in the \((\rho(|B|), \omega)\) plane convergence domains associated with \(p\)-cyclic, consistently ordered matrices for any order \(p \geq 3\). The current authors further assume that the eigenvalues of \(B^p\) are real and one-signed and show how to derive exact convergence domains in the \((\rho(B), \omega)\) plane in both the nonnegative and nonpositve cases for all \(p \geq 3\).