【作者】 马壮；

【导师】 陈国庆；

【作者基本信息】 内蒙古大学 ， 运筹学与控制论， 2005， 硕士

【摘要】 本文研究巨型稀疏系统的行作用法。利用行作用法的观点重新分析了求解线性方程组的传统Jacobi迭代法,Gauss-Seidel迭代法和SOR迭代法。引出一个用于求解系数矩阵半正定(不必对称)线性方程组的行作用法,并按统一的思路给出它们的收敛性证明。提出了一个具有较好数值实算性能,但收敛性尚未解决的行作用算法,通过数值实验对这几种算法的实际计算性能进行了分析、比较。本文还总结了求解线性不等式组、凸可行问题及凸不等式问题的行作用法,并给出一个一般的收敛性证明。给出精确求解二维Cutting-Stock问题的行作用法,通过数值实验表明了算法的可行性。更多还原

【Abstract】 This article mainly studies the row-action methods for huge and sparse systems. By using the concept of the row-action methods, the Jacobi iterative method, the Gauss-Seidel iterative method and the SOR iterative method for solving the system of linear equations are reanalyzed, a row-action method for solving the system of linear equations with positive semidefinite coefficient matrix (not necessarily symmetric) is derived, the convergence of these methods are proved by a unified approach. A new row-action method for solving the system of linear equations with positive semidefinite matrix (not necessarily symmetric) is considered, the numerical experiments show the method is very effective, however, its theoretical convergence is not proved yet. Based on summarizing the row-action methods for solving the system of linear inequalities and the convex feasibility problems, a row-action method for exactly solving the two-dimensional cutting-stock problems is presented, the availability of the method is shown by numerical examples.更多还原