Introduced is a kind of space uniform rational spline curve, which possesses tension parameters and is based on hyperbolic spline functions. A necessary and sufficient condition for the curve being torsion curve in every sub-interval is given. 引入了基于双曲样条函数的、具有张力参数的空间有理等距节点样条参数曲线,给出了这种曲线在每个样条子区间上为挠曲线段(即非平面曲线)的充分必要条件;
In the algorithm, as interval dichotomy and extended interval division are used, it is certain that all sub-interval boxes can be examined to guarantee all real roots of system of nonlinear equation can be attained. 在算法中,由于采用了区间二分法和区间扩展除法,可以对根可能存在的区间进行判断从而求出多变元非线性方程组的全部实根。
Interval section tells out all the sub-intervals which contain unique solution and the point section converges to the approximation of the exact solution in each sub-interval. 区间求解部分有保证地给出所有的含有唯一解的子区间;后续点迭代部分在各子区间中收敛到满足精度的各实值解的近似值。
To reflect the singularity of the solution, in the first sub-interval, we approximate the unknown functions by using non-polynomial functions, while in the remaining sub-intervals, we still use polynomial functions ap-proximate the unknowns. 为了反映解的奇异性,我们在第一个子区间使用非多项式函数逼近未知函数,而在剩下的子区间使用多项式逼近未知函数。