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《Numerical Mathematics A Journal of Chinese Universities》 1995-02
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THE UNIFORMITY OF SPLINE INTERPOLATING OPERATORS AND THE BEST OPERATORS OF INTERPOLATING APPROXIMATION IN REPRODUCING KERNEL SPACES

Deng Caixia Deng Zhongxing (Harbin University of Science & Technology)  
To guarantee uniform convergence, higher smooth conditions are genereally required for splines of differential operators, and at least, differential condition of the second order, for polynomial splines. This paper has combined splines of differential operators with reproducing kernel functions in H10 space of reproducing kernel and has shown the uniformity between these splines of differential operators and operators of the best interpolating approximation in H10, from which the uniform convergence of absolutely smooth functions is obtained for a type of differential operator of the second order in H10. A useful computational method is given in application for the approximation solution of linear differential equations of the second order with the boundary value problems of kind one.
【CateGory Index】: O241.3
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