中文摘要：

A family of piecewise rational quintic interpolation is presented. Each interpolation of the family, which is identified uniquely by the value of a parameter αi, is of C2 continuity without solving a system of consistency equations for the derivative values at the knots, and can be expressed by the basis functions. Interpolant is of O(hr) accuracy when f(x)?Cr[a,b], and the errors have only a small floating for a big change of the parameter αi, it means the interpolation is stable for the parameter. The interpolation can preserve the shape properties of the given data, such as monotonicity and convexity, and a proper choice of parameter αi is given.

英文摘要：

A family of piecewise rational quintic interpolation is presented. Each interpolation of the family, which is identified uniquely by the value of a parameter ai, is of C^2 continuity without solving a system of consistency equations for the derivative values at the knots, and can be expressed by the basis functions. Interpolant is of O（h^r） accuracy when f（x）∈C^r[a,b], and the errors have only a small floating for a big change of the parameter ai, it means the interpolation is stable for the parameter. The interpolation can preserve the shape properties of the given data, such as monotonicity and convexity, and a proper choice of parameter ai is given.