一类非线性方程组的Newton-GPHSS方法

Newton-GPHSS Methods for a Class of Systems of Nonlinear Equations

广义的预条件HSS(GPHSS)迭代方法是求解大型稀疏非Hermite正定线性代数方程组的有效方法.将其作为不精确Newton方法的内迭代求解算法,本文提出了一类Jacobi矩阵在解x*处为大型稀疏非Hermite矩阵的非线性方程组的Newton-GPHSS方法,给出了这类不精确牛顿法的局部收敛性定理.大量数值实验证明了该方法是正确有效的.

Generalized preconditioned Hermitian/skew-Hermitian splitting （GPHSS） iteration method is an efficient method for solving large sparse non-Hermitian positive definite system of linear equations. By making use of GPHSS method as the inner solver of inexact Newton method, a class of Newton-GPHSS methods for solving large sparse systems of nonlinear equations with positive definite Jacobi matrices at the solution points is proposed. The local convergence theorem of this class of inexact Newton methods is given. Numerical results confirm that the proposed method is correct and efficient.