Construction Techniques For Highly Accurate Quasi-interpolation Operators And Its Application

This thesis can be divided into four parts.The first part simply presents the back-ground and current research situation concerning the problem.The second part introduces the definition of B-Spline and MQ-B-Spline,some of their important properties and the linear polynomial reproduction property of the Greville point on the basis of B-Spline and MQ-B-Spline;Generalized Greville Point is introduced and the high degree polynomial reproduction on the basis of B-Spline and high degree quasi polynomial reproduction on the basis of MQ-B-Spline is proved;Generalized Greville point is modified to possess high degree polynomial reproduction.A method is given in the third part,which is based on the properties of Generalized Greville point,modified General-ized Greville point and least square method;With the method,the quasi-interpolation operators L_h,Q_h,(?)_h,(?)_h and(?)_h are constructed to show they authentically possess highly accurate approximation property.In the last part,firstly the highly approximation property of the operators is illuminated theoretically,and the numerical experiment is done to posterior estimate.