On the sharpness of some upper bounds for the spectral radii of S.O.R. iteration matrices

DOI10.1007/BF01396371zbMath0453.65021MaRDI QIDQ1149232

Richard S. Varga, Michael Neumann

Publication date: 1980

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/186277

zbMATH Keywords

upper boundsspectral radiussplittingH-matrixrelaxation methodsgeneralized S.O.R. methodhermitian positive definite matricesskew- hermitian matrix

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57) Iterative numerical methods for linear systems (65F10)

Related Items (10)

On the convergence of the unsymmetric successive overrelaxation (USSOR) method ⋮ A convergence analysis of block accelerated over-relaxation iterative methods for weak block \(H\)-matrices to partition \(\pi \) ⋮ Superior convergence domains for a \(p\)-cyclic SSOR majorizer ⋮ An iterative method applied to nonsymmetric linear systems ⋮ The Kahan S.O.R. convergence bound for nonsingular and irreducible M- matrices ⋮ On bounds for the convergence of the SSOR method forH-matrices ⋮ Neighborhoods of Dominant Convergence for the SSOR Method ⋮ On minimization of upper bound for the convergence rate of the QHSS iteration method ⋮ Exact convergence and divergence domains for the symmetric successive overrelaxation iterative (SSOR) method applied to H-matrices ⋮ p-cyclic matrices and the symmetric successive overrelaxation method

Cites Work

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• \(p\)-cyclic matrices: A generalization of the Young-Frankel successive overrelaxation scheme
• On recurring theorems on diagonal dominance
• Über reguläre Zerlegungen von Matrizen und einige Anwendungen
• Generalised consistent ordering and the optimum successive overrelaxation factor
• Über die Konvergenz des Relaxationsverfahrens bei nicht-negativen und diagonal-dominanten Matrizen
• Generalized Overrelaxation and Gauss-Seidel Convergence on Hilbert Space
• Gauss–Seidel Convergence for Operators on Hilbert Space

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