解矩阵方程的一种多项式预处理技术

先引入多项式预处理技术，用一次插值多项式法构造出一个合理的多项式预处理矩阵并对矩阵方程进行预处理，这样不仅可以缩小矩阵的奇异值的分布范围，而且能达到改善其奇异值比的目的；然后给出了新的算法，并分析了该算法的收敛速率的估计式，此估计式表明，只要采用恰当的预处理技术就可显著地提高迭代法的收敛速度；最后给出了数值例子，结果说明经过预处理后的矩阵方程比原来的矩阵方程的收敛速度更快，这充分表明了矩阵方程在多项式结构的预处理矩阵下求解速度的优越性，也说明通过一次插值多项式的构造来选取预处理矩阵是可行的.

Polynomial Preconditioning Technique for Matrix Equation

Firstly the polynomial preconditioning technique and an interpolation polynomial method are considered for constructing a proper polynomial preconditioners to transform the system.This reduces the distribution range of singular value and improves the ratio of singular value.Besides,a new algorithm is given and the convergence of the algorithm is analysed.The expression of estimation about convergence rate testifies that this algorithm can improve the convergence rate of iterative methods significantly if a ...