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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Determination of the $D^ {1/2}$-norm of the SOR iterative matrix for the unsymmetric case
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by D. J. Evans and C. Li PDF
Math. Comp. 53 (1989), 203-218 Request permission


This paper is concerned with the determination of the Jordan canonical form and ${D^{1/2}}$-norm of the SOR iterative matrix derived from the coefficient matrix A having the form \[ A = \left ( {\begin {array}{*{20}{c}} {D1} \hfill & { - H} \hfill \\ {{H^T}} \hfill & {{D_2}} \hfill \\ \end {array} } \right )\] with ${D_1}$ and ${D_2}$ symmetric and positive definite. The theoretical results show that the Jordan form is not diagonal, but has only q principal vectors of grade 2 and that the ${D^{1/2}}$-norm of ${\mathcal {L}_{{\omega _b}}}$ (${\omega _b}$, the optimum parameter) is less than unity if and only if $\bar \mu = \rho (B)$, the spectral radius of the associated Jacobi iterative matrix, is less than unity. Here q is the multiplicity of the eigenvalue $i\bar \mu$ of B.
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 53 (1989), 203-218
  • MSC: Primary 65F10; Secondary 65N99
  • DOI:
  • MathSciNet review: 969486