论列选主元法在Gauss-Seidel迭代法和SOR迭代中的应用

On the Application of Column Pivot Element in Gauss-Seidel and SOR Iteration

将迭代法与列选主元的思想相结合,基于Gauss-Seidel迭代法和SOR迭代法,给出了两种改进的解线性方程组的迭代算法.所给的方法扩大了Gauss-Seidel迭代法、SOR迭代法的使用范围,进而使其具有很好的现实应用价值.编写了MATLAB程序对改进的两种Gauss-Seidel迭代法、SOR迭代法进行了验证,同时,通过算例对经典的Gauss-Seidel迭代法、SOR迭代法与改进后的Gauss-Seidel迭代法、SOR迭代法的收敛性以及收敛速度进行了比较.算例结果表明:改进的两种迭代算法相对于原来的Gauss-Seidel迭代法和SOR迭代法,具有使用范围较广,收敛速度更快的优点。

Combining the iterative method and the column pivoting,two improved iterative methods for linear equations is given,based on the Gauss-Seidel iterative method and SOR iterative method.The improved method expands the range to the Gauss-Seidel iterative method and SOR iterative method,which brings practical application value.By writing MATLAB program,the convergence of Gauss-Seidel iterative and the SOR iterative methods are verified.Meanwhile,through to comparison of the convergence speed of the classical Gauss-Seidel iterative,SOR iterative method,the improved Gauss-Seidel iterative method,and SOR iterative method,a conclusion is given： the two new iterative methods has a wider scope,a faster convergence speed.