【摘要】 研究了三次样条插值的小波插值函数 ,证明了在给定的插值节点上的小波插值函数是三次样条函数空间中的最佳逼近函数 .给出插值函数的误差估计式 ,提出了用两个一阶导算子矩阵替换二阶导算子矩阵的替代算法 ,并对Burgers方程进行了验算 .更多还原

【Abstract】 The optimal approximation property is shown when the cubic spline interval wavelet is used in the interpolation with some special points. This property ensures the identical of the interpolation by use of scale basis and of wavelet basis. The interpolation error is also discussed. A new algorithm is presented in which two one-order differential matrixes are used to substitute for the two-order one. This way produces less vibration for the numerical solution of Burgers equation when the coefficient is somewhat larger.更多还原