在Mathematica中实现Newton-Raphson迭代

为了寻找方程

可以使用Newton-Raphson迭代方法：

NRIter[func_, xzero_, n_ : 5] :=Module[{pointlist = {}, x, xold = xzero, xnew, f, df, xl, xr, k},f[x_] = func[x];df[x_] = D[func[x], x];Do[(pointlist = Join[pointlist, {{xold, 0}}, {{xold, f[xold]}}];xnew = xold - f[xold]/df[xold];xold = xnew),{k, 1, n}];xl = Min[First[Transpose[pointlist]]] - 0.5;xr = Max[First[Transpose[pointlist]]] + 0.5;Plot[f[x], {x, xl, xr}, PlotRange -> All,PlotStyle -> {{Thickness[0.001], Dashing[{0.005, 0.005}]}},Epilog -> {Thickness[0.001], Line[pointlist]}]]NRIter[(#^3 + #^2 - 3) &, 3.5]

NRIter[Sin, 1.404091, 10]