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In this paper, the linear complementarity problem : review of research trends at home and abroad , first introduced the basic iterative method for linear systems , such as Jacobi, Gauss -Seidel , overrelaxation iterative method , fast overrelaxation iterative method : then introduced two equivalent forms of the linear complementarity problem , both equivalent form method for solving linear equations can be applied . Then, the linear complementarity problems AOR MAOR GAOR , and a two-stage iterative method ; Finally , when the system matrix M P matrix lists the range of error bounds given in the literature , the linear complementarity problem . According to the research results at home and abroad , the paper mainly studied a special class of generalized linear complementarity problems Alefeld G , Wang ZY Shen ZH linear complementarity problem interval iterative method of promotion ; such linear the complementarity problem solution interval boundaries algorithm , its main computational workload simplify solving linear systems . That is, when the generalized linear complementarity problems , the system matrices A, B L matrix strictly diagonally dominant , application interval iterative method , an effective algorithm is given , to take advantage of the computer 's high-speed computing and parallel computing , get a nested sequence . Unique solution , iterative sequence interval the radius gradually reduced , approaching the sole solution . When the error condition is reached , whichever interval midpoint for the approximate solution , or the conclusion that no solution .
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