论文标题
平行于牛顿 - 切尔比瑟夫的多项式预处理，用于共轭梯度法
Parallel Newton-Chebyshev Polynomial Preconditioners for the Conjugate Gradient method
论文作者
论文摘要
在本说明中，我们利用多项式预处理使用共轭梯度方法来解决平行环境中大型对称正定线性系统。我们将一种专业的牛顿方法求解，以求解矩阵方程x^{ - 1} = a和chebyshev多项式进行预处理。我们提出了一个简单的修改一个参数，该参数避免了极端特征值的聚类，以加快收敛性。我们在平行的环境中提供了非常大的矩阵（最多80亿未知数）的结果，以显示拟议的预处理类的效率。
In this note we exploit polynomial preconditioners for the Conjugate Gradient method to solve large symmetric positive definite linear systems in a parallel environment. We put in connection a specialized Newton method to solve the matrix equation X^{-1} = A and the Chebyshev polynomials for preconditioning. We propose a simple modification of one parameter which avoids clustering of extremal eigenvalues in order to speed-up convergence. We provide results on very large matrices (up to 8 billion unknowns) in a parallel environment showing the efficiency of the proposed class of preconditioners.
