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    STUDIA MATHEMATICA - Issue no. 4 / 2008  
         
  Article:   THE WEIGHTED SPLINE QUASI-INTERPOLANT OPERATORS.

Authors:  MAGNOLIA TILCA. 		 
       
         
  Abstract:   A new quasi-interpolant operator starting from the operator described by Sablonnière [1], [7] is presented here. The operator is a linear combination of some linear functionals and normalized B-spline functions. If Sablonièr uses the arithmetic mean of the consecutive given points, the linear functionals presented here use the mesh points chosen as the weighted arithmetic mean of given points from the interval [a, b]. The article describes the way of computing the quadratic and cubic weighted spline quasi-interpolant operators and underlines the good numerical approximation of these new operators using implemented Matlab functions. The fact that the cubic weighted spline quasi-intepolant operators are a completion of the cubic spline quasi-interpolant operators offering a better approximation, but only among some intervals, is proven in the last section of the paper.  
         
     
         
         
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