A multiplicative Schwarz iteration scheme for solving the linear complementarity problem with an \(H\)-matrix

DOI10.1016/j.laa.2008.10.005zbMath1166.65031OpenAlexW2042771459MaRDI QIDQ999791

Haijian Yang, Hong-Ru Xu, Qing-Guo Li

Publication date: 10 February 2009

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

Full work available at URL: https://doi.org/10.1016/j.laa.2008.10.005

zbMATH Keywords

algorithmconvergencelinear complementarity problemnumerical experimentsweighted max-norm\(H_{+}\)-matrixalgebraic multiplicative Schwarz iteration

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Iterative numerical methods for linear systems (65F10)

Related Items (5)

Parallel multiplicative Schwarz preconditioner for solving nonselfadjoint elliptic problems ⋮ Overlapping restricted additive Schwarz method applied to the linear complementarity problem with an \(H\)-matrix ⋮ Overlapping restricted additive Schwarz method with damping factor for \(H\)-matrix linear complementarity problem ⋮ Additive and restricted additive Schwarz-Richardson methods for inequalities with nonlinear monotone operators ⋮ The primal-dual active set method for a class of nonlinear problems with \(T\)-monotone operators

Cites Work

• Overlapping additive and multiplicative Schwarz iterations for \(H\)-matrices
• Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications
• \(H\)-splittings and two-stage iterative methods
• Chaotic iterative methods for the linear complementarity problems
• Nonnegative splitting theory
• Curvature based image registration
• Weighted max norms, splittings, and overlapping additive Schwarz iterations
• The alternating Schwarz method applied to some biharmonic variational inequalities
• Multigrid Algorithms for Variational Inequalities
• On the monotone convergence of matrix multisplitting relaxation methods for the linear complementarity problem
• Two-level Schwarz method for unilateral variational inequalities
• On Monotone and Geometric Convergence of Schwarz Methods for Two-Sided Obstacle Problems
• On the Convergence of the Multisplitting Methods for the Linear Complementarity Problem
• A comparison result for multisplittings and waveform relaxation methods
• Parallel solutions of variational inequality problems with nonlinear source terms
• Two-stage Multisplitting Methods with Overlapping Blocks
• Weighted max-norm estimate of additive Schwarz iteration scheme for solving linear complementarity problems
• Algebraic theory of multiplicative Schwarz methods
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