摘要
对于非线性方程组F(x)=0,Newton迭代公式x(k+1)=x(k)-[F′(x(k))]-1F(x(k)),(k=0,1,2,…)形式简单且超线性收敛,但它对初值依赖性强且每次迭代都需要计算Jacobi矩阵及其逆矩阵,大计算量易导致误差累积传播.通过对Newton迭代公式的改进,得到BFS秩2拟Newton方法,通过一具体例子,在收敛速度上与逆Broyden秩1方法进行比较,特定条件下,BFS秩2方法比逆Broyden秩1方法收敛速度快,在MATLAB7.5环境中验证了BFS秩2方法是数值稳定的.
For the nonlinear equations F （x） = 0, the Newton iteration formulation x^（k＋1）=x^（k）-[F＇（x^（k））]^-1F（x^（k））,（k=0,1,2,…）has a simple form and superlinear convergence, but it strongly depends on the initial value, requires calculating Jaeobian matrix and its inverse matrix to realize each alternation, and the large amount of calculation easily leads to the accumulated errors. Through the improving of Newton iterative formula, it obtains the rank -two BFS quasi Newton method. Compared with the single rank inverse Broyden method at the convergence rate and under given conditions, the convergence rate of rank - two BFS method is faster. It is also verified by using an idiographic example that the rank -two BFS method is stable in MATLAB7.5.
出处
《云南民族大学学报（自然科学版）》
CAS
2009年第3期213-217,共5页
Journal of Yunnan Minzu University:Natural Sciences Edition
