非线性方程组的逆Broyden秩1拟Newton方法及其在MATLAB中的实现

Single rank inverse Broyden quasi Newton method and its realization in MATLAB for nonlinear equations

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,…)的最大优点在于其形式简单且是超线性收敛的,而最大的缺点在于对初值依赖性强且每一次迭代均需要计算Jacobi矩阵及其逆矩阵,计算量大,易导致误差累积传播.通过对Newton迭代公式的逐步改进,展现了逆Broy-den秩1拟Newton方法的形成过程,并以一具体例子,实现该方法在MATLAB7.5环境中的数值求解过程.

For the nonlinear equations F(x)=0,the advantages of Newton iteration formulation x(k+1)=x(k)-[F′(x(k))]-1F(x(k))(k=0,1,2,…) lie in its simple form and superlinear convergence,while the disadvantages include its strong dependence on initial value,requiring calculation Jacobian matrix and its inverse matrix to realize each alternation,and the large amount of calculation easily lead to accumulate and spread errors.Through the improving to Newton iterative formula step by step,the forming process of single ran...