p-cyclic matrices and the symmetric successive overrelaxation method

DOI10.1016/0024-3795(84)90223-4zbMath0569.65022OpenAlexW2076220511MaRDI QIDQ1060806

Richard S. Varga, Wilhelm Niethammer, Da-Yong Cai

Publication date: 1984

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(84)90223-4

zbMATH Keywords

SSORsymmetric successive overrelaxationH-matricesintervals of convergence and divergenceweakly cyclic Jacobi matrix

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

Related Items (30)

A note on the eigenvalue relationship for USAOR iterative method applied to \(p\)-cyclic matrices ⋮ Generalized consistent orderings and the accelerated overrelaxation method ⋮ Zur Konvergenz des SSOR-Verfahrens für nichtlineare Gleichungssysteme. (Convergence of the SSOR method for nonlinear systems of simultaneous equations) ⋮ Sets of convergence and stability regions ⋮ Stepsize restrictions for stability in the numerical solution of ordinary and partial differential equations ⋮ A survey of the iterative methods for the solution of linear systems by extrapolation, relaxation and other techniques ⋮ 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 ⋮ A necessary and sufficient condition for semiconvergence and optimal parameter of the SSOR method for solving the rank deficient linear least squares problem ⋮ On the exact \(p\)-cyclic SSOR convergence domains ⋮ A note on the SSOR convergence domain due to Neumaier and Varga ⋮ Precise domains of convergence for the block SSOR method associated with p-cyclic matrices ⋮ A note on the SSOR and USSOR iterative methods applied to p-cyclic matrices ⋮ Towards the determination of the optimal \(p\)-cyclic SSOR ⋮ Sor and related methods forp-cyclic systems ⋮ Domains of divergence of the USSOR method applied on p-cyclic matrices ⋮ Convergence analysis of the parallel multisplitting psd method ⋮ On the convergence of the modified accelerated overrelaxation (MAOR) method ⋮ Symmetric block-SOR methods for rank-deficient least squares problems ⋮ Neighborhoods of Dominant Convergence for the SSOR Method ⋮ The convergence of the two-block SAOR method for least-squares problems ⋮ On domains of superior convergence of the SSOR method to that of the SOR method ⋮ The impact of eigenvalue locality on the convergence behavior of the PSD method for two-cyclic matrices ⋮ Convergence domains of the SSOR method for a class of generalized consistently ordered matrices ⋮ Convergence of preconditioned iterative methods ⋮ Successive overrelaxation (SOR) and related methods ⋮ Exact convergence and divergence domains for the symmetric successive overrelaxation iterative (SSOR) method applied to H-matrices ⋮ On the analysis of the unsymmetric successive overrelaxation method when applied to p-cyclic matrices ⋮ Some recent results on the modified SOR theory ⋮ Relationship of eigenvalues for USAOR iterative method applied to a class of \(p\)-cyclic matrices

Cites Work

• Unnamed Item
• Unnamed Item
• On the successive over-relaxation method for cyclic operators
• On the sharpness of some upper bounds for the spectral radii of S.O.R. iteration matrices
• Zur Konvergenz des symmetrischen Relaxationsverfahrens
• On recurring theorems on diagonal dominance
• Generalised consistent ordering and the optimum successive overrelaxation factor
• Relaxation bei komplexen Matrizen
• On bounds for the convergence of the SSOR method forH-matrices
• The S.S.O.R. Iteration Scheme for Equations with  1 Ordering
• On the equivalence of SOR, SSOR and USSOR as applied to  1-ordered systems of linear equations

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