MATLAB 牛顿下山法的一个小程序，原理就不详细说了。因牛顿迭代法受初值选取的限制，为防止迭代发散，对迭代过程再附加一项要求:|f(x(k+1))|<|f(x(k))|,将牛顿法迭代的结果:x(k+1) =x(k)-f(x(k))/f (x(k))和前一近似值x(k)适当加权平均做为新的改进值:x(k+1)=u*x(k+1) +(1-u)*x(k),其中u(0<>



迭代时u取1开始，逐次减半计算，直至附加要求符合为止。实例计算中x(k)=x(0)不变，只更新u和x(k+1)，直至:|f(x(k+1))|<|f(x(k))|（即|f(x(1))|<|f(x(0))|)，然后更新下山因子为u=1,继续以牛顿法迭代。-MATLAB Newton-down a small program, the principle is not explained in detail. Newton iteration by the initial value of the selected limit, in order to prevent additional iterative divergence, the iterative process a request: | f (x (k+1)) | < | f (x (k)) | Newton iteration Results: x (k+1) ' = X (k)-f (x (k))/f'　(x (k)) and a previous approximation x (k), appropriately weighted average as a new improved value: x (k+1 ) = u* x (k+1) ' + (1-u)* x (k), where u (0 < u>　iteration take successive calculated at 50　until the additional requirements found so far. examples of calculation of X ( k) = x (0) unchanged profile u and x (k+1, hungry) until: | f (x (k+1)) | < | f (x (k)) | (i.e. | f (x (1)) | < | f (x (0)) |), then profile downhill factor for u = 1, to continue to Newton iteration.