中文摘要：

通过分析常用的求解非线性问题的数值方法,提出一类具强烈几何背景的多点曲线法。多点曲线法不仅具有超二次收敛的特性,而且避免了高阶导数,其收敛域比高阶非Newton法的收敛域有明显改善。数值算例结果表明多点曲线法在奇异非线性方程和非线性方程组求解等问题中非常实用。

英文摘要：

By analyzing the traditional numerical methods of solving nonlinear equations, a kind of multi-point curve methods which have strong geometric background were presented. This kind of methods not only have super-quadratic convergence, but also can iterate without higher derivatives. Furthermore, the convergent fields of these new methods are obviously improved compared with higher order non-Newton method. The numerical results show that the presented method is effective in solving singular nonlinear equation and nonlinear systems of equations.