Block cyclic SOR for Markov chains with \(p\)-cyclic infinitesimal generator

DOI10.1016/0024-3795(91)90377-9zbMath0736.65094OpenAlexW2047567338MaRDI QIDQ1176521

William J. Stewart, Kimon P. Kontovasilis, Robert J. Plemmons

Publication date: 25 June 1992

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

Full work available at URL: https://doi.org/10.1016/0024-3795(91)90377-9

zbMATH Keywords

numerical testsblock successive overrelaxationoptimal convergence rateconvergence intervalsirreducible Markov chainstationary probability distributionp-cyclic iterations

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Iterative numerical methods for linear systems (65F10) Probabilistic methods, stochastic differential equations (65C99)

Related Items (15)

Is the optimal \(\omega\) best for the SOR iteration method? ⋮ Superior convergence domains for a \(p\)-cyclic SSOR majorizer ⋮ Exact SOR convergence regions for a general class of \(p\)-cyclic matrices ⋮ Optimal \(p\)-cyclic SOR for complex spectra ⋮ Towards the determination of the optimal \(p\)-cyclic SSOR ⋮ Application of the Schur-Cohn theorem to the precise convergence domain for a \(p\)-cyclic SOR iteration matrix ⋮ A massively parallel algorithm for bordered almost block diagonal systems on GPUs ⋮ Semiconvergence of block SOR method for singular linear systems with \(p\)-cyclic matrices ⋮ Conference celebrating the 60th birthday of Robert J. Plemmons. Papers from the conference, Winston-Salem, NC, USA, January 1999 ⋮ Dedication to Robert J. Plemmons ⋮ A Young-Eidson's type algorithm for complex \(p\)-cyclic SOR spectra ⋮ A note on the extended convergence of SOR for two-periodic Markov chains ⋮ Successive overrelaxation (SOR) and related methods ⋮ Optimal stretched parameters for the SOR iterative method ⋮ Convergence theory of some classes of iterative aggregation/disaggregation methods for computing stationary probability vectors of stochastic matrices

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Over- and underrelaxation for linear systems with weakly cyclic Jacobi matrices of index p
• \(p\)-cyclic matrices: A generalization of the Young-Frankel successive overrelaxation scheme
• Optimal successive overrelaxation iterative methods for \(p\)-cyclic matrices
• Convergence of block iterative methods applied to sparse least-squares problems
• k-step iterative methods for solving nonlinear systems of equations
• Block iterative algorithms for stochastic matrices
• Some new characterizations of the Chebyshev polynomials
• Optimality relationships for p-cyclic SOR
• On the Optimization of the Classical Iterative Schemes for the Solution of Complex Singular Linear Systems
• Relaxations for the numerical solutions of some stochastic problems
• Best Cyclic Repartitioning for Optimal Successive Overrelaxation Convergence
• Stochastic Complementation, Uncoupling Markov Chains, and the Theory of Nearly Reducible Systems
• Iterative Methods for Solving Partial Difference Equations of Elliptic Type

This page was built for publication: Block cyclic SOR for Markov chains with \(p\)-cyclic infinitesimal generator