A relaxation accelerated two-sweep modulus-based matrix splitting iteration method for solving linear complementarity problems

求解大规模稀疏线性互补问题的移位分裂多参数模迭代法

Solving Large-Scale Sparse Linear Complementarity Problems Using a Relaxed Shifted Matrix-Splitting Modulus-Based Iteration Method

提出移位分裂多参数模迭代法求解大规模稀疏线性互补问题，通过引入额外参数并建立收敛条件，数值实验表明其在迭代次数、残差和CPU时间上优于现有方法。

More on Modulus Based Iterative Method for Solving Implicit Complementarity Problem

This article presents a class of modified new modulus-based iterative methods to process the large and sparse implicit complementarity problem (ICP). By using two positive diagonal matrices, we formulate a fixed-point equation which is equivalent to an ICP and based on a fixed-point equation, an iterative method is presented to solve the ICP. We provide some convergence conditions for the proposed methods when the system matrix is a $P$-matrix or an $H_+$-matrix.

求解大型稀疏线性互补问题的新型加速模基迭代方法

New Accelerated Modulus-Based Iteration Method for Solving Large and Sparse Linear Complementarity Problem

针对线性互补问题，本文提出新型加速模基迭代方法，在系统矩阵为$H_+$-矩阵时给出收敛准则，数值实验验证其可减少迭代次数与CPU时间、提升收敛性能。

基于新型松弛模的迭代方法求解大型稀疏隐互补问题

New Relaxation Modulus Based Iterative Method for Large and Sparse Implicit Complementarity Problem

针对大型稀疏隐互补问题，提出基于两个正对角矩阵构造不动点方程的新型松弛模迭代方法，证明其等价性，并在$P$-矩阵和$H_+$-矩阵条件下建立收敛性。

Sparsity Exploitation of Accelerated Modulus-Based Gauss-Seidel Method for Interactive Rigid Body Simulations

Large-scale linear complementarity problems (LCPs) are repeatedly solved in interactive rigid-body simulations. The projected Gauss-Seidel method is often employed for LCPs, since it has advantages in computation time, numerical robustness, and memory use. Zheng and Yin (2013) proposed modulus-based matrix splitting iteration methods and showed their effectiveness for large problems, but a simple application of their approach to large-scale LCPs in interactive rigid-body simulations is not effective since such a simple application demands large matrix multiplications. In this paper, we propose…