论文标题
面向对象的C ++库QIBSH ++用于HERMITE样条形插值
The Object Oriented c++ library QIBSH++ for Hermite spline Quasi Interpolation
论文作者
论文摘要
库QIBSH ++是用于解决准插值问题的C ++对象库。该库基于HERMITE准插值操作员，该操作员被推导为用于用于普通微分方程边界值问题的数值解决方案的线性多步法方法的连续扩展。该库包括使用HERMITE数据或将有限差分方案应用于衍生值时，当衍生值无法直接可用时。还实施了通过张量产品技术将准插值程序概括为表面和体积近似。该方法也已被概括为一维矢量数据，周期性数据以及圆柱坐标中的二维数据，相对于角度参数周期性。数值测试表明，在许多实际问题中可以有效地使用该库。
The library QIBSH++ is a C++ object oriented library for the solution of Quasi Interpolation problems. The library is based on a Hermite Quasi Interpolating operator, which was derived as continuous extensions of linear multistep methods applied for the numerical solution of Boundary Value Problems for Ordinary Differential Equations. The library includes the possibility to use Hermite data or to apply a finite difference scheme for derivative approximations, when derivative values are not directly available. The generalization of the quasi interpolation procedure to surfaces and volumes approximation by means of a tensor product technique is also implemented. The method has been also generalized for one dimensional vectorial data, periodic data, and for two dimensional data in cylindrical coordinates, periodic with respect to the angular argument. Numerical tests show that the library could be used efficiently in many practical problems.
